State Design Pattern: How to avoid code duplication when using entry() and exit()?

Situation: My States have an entry() and exit() method that needs to be called every time when a State transitions. To ensure that, I used a changeState() method in State that contains the necessary procedure. It is called by the Context every time it uses an operation involving the state machine. The problem however, is that I need to call state.changeState() every time when I add a new method and I'm sure there's a way to avoid that code duplication. Below is code for further clarification

class Context {
    State state;

    void method1() {
        state.method1();
        state.changeState();
    }

    void method2() {
        state.method2();
        state.changeState(); // Code duplication!!
}

abstract class State {
    Context context;
    State next;

    void changeState() {
        this.exit();
        next.entry();
        context.setState(next);
    }
    // other necessary methods
}

class ConcreteState extends State {
    void method1() {
        // do something
        next = AnotherConcreteState;
    }
    void entry() {/*do something */};
    void exit() {/*do something */};
}

If I want to add additional methods in Context, what can I do to avoid code duplication of calling state.changeState() every time inside the new methods?

You are very close. The changeState method belongs in the Context class, not the State class. Here's a good article on the topic. Note that the class diagram shows changeState in the Document (context) class.

To make it even cleaner, changeState could take the next state as a parameter. Like this:

class Context {
  State state;

  void method1() {
    state.method1();
  }

  void changeState(next) {
    state.exit();
    this.state = next;
    state.enter();
  }
}

abstract class State {
  Context context;

  // other methods
}

class ConcreteState extends State {
  void method1() {
    // do something
    context.changeState(AnotherConcreteState);
  }

  void enter() { /* do something */ }
  void exit() { /* do something */ }
}

Now, as you add more methods to Context, there is no duplication in Context. It'd look like this:

class Context {
  State state;

  void method1() {
    state.method1();
  }

  void method2() {
    state.method2();
  }

  void changeState(next) {
    state.exit();
    this.state = next;
    state.enter();
  }
}

abstract class State {
  Context context;

  // other methods
}

class ConcreteState extends State {
  void method1() {
    // do something
    context.changeState(AnotherConcreteState);
  }

  void method2() {
    // do something else
    context.changeState(YetAnotherConcreteState);
  }

  void enter() { /* do something */ }
  void exit() { /* do something */ }
}