Right Drawer - how to add Toolbar button?

I have extended the well-known Google Navigation Drawer Example by adding Toolbar and right-side Drawer in a simple test project at GitHub:

How to add a "burger" button to the Toolbar - which would open the right Drawer (currently you can only swipe it with a finger)?

The "burger" button for the left Drawer is already there and works well (probably added by ActionBarDrawerToggle?)

Here is my current activity_main.xml:

<android.support.v4.widget.DrawerLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:id="@+id/drawer_layout"
    android:layout_width="match_parent"
    android:layout_height="match_parent">

    <LinearLayout 
        android:orientation="vertical"
        android:layout_width="match_parent"
        android:layout_height="match_parent">

        <android.support.v7.widget.Toolbar 
            xmlns:android="http://schemas.android.com/apk/res/android"
            android:id="@+id/toolbar"
            android:layout_width="match_parent"
            android:layout_height="wrap_content" />

        <FrameLayout
            android:id="@+id/content_frame"
            android:layout_width="match_parent"
            android:layout_height="match_parent" />

    </LinearLayout>

    <ListView
        android:id="@+id/left_drawer"
        android:layout_width="240dp"
        android:layout_height="match_parent"
        android:layout_gravity="start"
        android:choiceMode="singleChoice" />

    <ListView
        android:id="@+id/right_drawer"
        android:layout_width="160dp"
        android:layout_height="match_parent"
        android:layout_gravity="end"
        android:choiceMode="singleChoice" />

</android.support.v4.widget.DrawerLayout>

And here is the MainActivity.java:

public class MainActivity extends AppCompatActivity {
    private Toolbar mToolbar;
    private DrawerLayout mDrawerLayout;
    private ListView mDrawerList;
    private ListView mActionList;
    private ActionBarDrawerToggle mDrawerToggle;

    private String[] mPlanetTitles;
    private String[] mActions;
    private int[] mIcons;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        mPlanetTitles = getResources().getStringArray(R.array.planets_array);
        mActions = getResources().getStringArray(R.array.music_actions);

        TypedArray ta = getResources().obtainTypedArray(R.array.music_icons);
        mIcons = new int[ta.length()];
        for (int i = 0; i < mIcons.length; i++)
            mIcons[i] = ta.getResourceId(i, R.drawable.ic_menu_black_24dp);
        ta.recycle();

        mToolbar = (Toolbar) findViewById(R.id.toolbar);
        setSupportActionBar(mToolbar);

        mDrawerLayout = (DrawerLayout) findViewById(R.id.drawer_layout);
        mDrawerList = (ListView) findViewById(R.id.left_drawer);
        mActionList = (ListView) findViewById(R.id.right_drawer);

        mDrawerList.setAdapter(new ArrayAdapter<String>(this,
            R.layout.drawer_list_item, mPlanetTitles) {
            @Override
            public View getView(int position, View convertView, ViewGroup parent) {
                TextView view = (TextView) super.getView(position, convertView, parent);
                view.setCompoundDrawablePadding(24);
                view.setCompoundDrawablesWithIntrinsicBounds(
                    R.drawable.ic_stars_white_24dp, 0, 0, 0);
                return view;
            }
        });

        mActionList.setAdapter(new ArrayAdapter<String>(this,
            android.R.layout.simple_list_item_1, mActions) {
            @Override
            public View getView(int position, View convertView, ViewGroup parent) {
                TextView view = (TextView) super.getView(position, convertView, parent);
                view.setCompoundDrawablePadding(24);
                view.setCompoundDrawablesWithIntrinsicBounds(mIcons[position], 0, 0, 0);
                return view;
            }
        });

        mDrawerToggle = new ActionBarDrawerToggle(
                this,                  /* host Activity */
                mDrawerLayout,         /* DrawerLayout object */
                mToolbar,
                R.string.drawer_open,  /* "open drawer" description for accessibility */
                R.string.drawer_close  /* "close drawer" description for accessibility */
                ) {
            public void onDrawerClosed(View view) {
                mToolbar.setTitle(mTitle);
                invalidateOptionsMenu(); // creates call to onPrepareOptionsMenu()
            }

            public void onDrawerOpened(View drawerView) {
                mToolbar.setTitle(mDrawerTitle);
                invalidateOptionsMenu(); // creates call to onPrepareOptionsMenu()
            }
        };
        mDrawerLayout.setDrawerListener(mDrawerToggle);

        if (savedInstanceState == null) {
            selectItem(0);
        }
    }

I did try the following 2 lines too - but they haven't changed anything (neither the left, nor the right buttons):

getSupportActionBar().setDisplayHomeAsUpEnabled(true);
getSupportActionBar().setHomeButtonEnabled(true);

you have to create custom toolbar like below :

 <android.support.v7.widget.Toolbar
        android:id="@+id/toolbar"
        android:layout_width="match_parent"
        android:layout_height="?attr/actionBarSize"
        android:background="?attr/colorPrimary"
        android:theme="@style/ThemeOverlay.AppCompat.Dark.ActionBar">

        <ImageView
            android:layout_width="wrap_content"
            android:src="@drawable/ic_menu"
            android:padding="@dimen/eight"
            android:id="@+id/ivCustomDrawable"
            android:adjustViewBounds="true"
            android:layout_height="wrap_content" />

        <TextView
            android:layout_width="wrap_content"
            android:textSize="20sp"
            android:text="Custom Toolbar"
            android:textColor="@android:color/white"
            android:layout_height="wrap_content" />

    </android.support.v7.widget.Toolbar>

and in Java file add this lines:

  private void setupToolbar() {
        Toolbar toolbar = (Toolbar) findViewById(R.id.toolbar);
        setSupportActionBar(toolbar);

        ivCustomDrawable = (ImageView) toolbar.findViewById(R.id.ivCustomDrawable);
        ivCustomDrawable.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
                drawerLayout.openDrawer(GravityCompat.START); //What ever your drawer gravity 
            }
        });

        ActionBar actionBar = getSupportActionBar();
        if (actionBar != null) {
            actionBar.setHomeAsUpIndicator(R.drawable.ic_menu);
            actionBar.setDisplayHomeAsUpEnabled(false);
            actionBar.setDisplayShowTitleEnabled(false);
        }
    }