How to sort python pandas dataframe in repetitive order after groupby?

I have a dataset which is sorted in this order:

I want it to be sorted in the following order:

I want the col2 to be in repetitive fashion, as in, for col1 'a' values, it should be 1,2,3,4 and then 1,2,3,4 again instead of 1,1,2,2,3,3,4,4. I have used the following code, but it is not working:

import pandas as pd

# Creating the DataFrame
data = {
    'col1': ['a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b'],
    'col2': [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6],
    'col3': ['r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'q', 'w', 'e']
}

df = pd.DataFrame(data)

# Sort by col1, then reorder col2 within each group
df_sorted = df.sort_values(by=['col1', 'col2']).reset_index(drop=True)

df_sorted = df_sorted.groupby('col1', group_keys=False).apply(lambda x: x.sort_values('col2'))

# Display the sorted dataframe
print(df_sorted)

Use groupby.cumcount to form a secondary key for sorting:

out = (df.assign(key=lambda x: x.groupby(['col1', 'col2']).cumcount())
         .sort_values(by=['col1', 'key', 'col2'])
         .drop(columns='key')
      )

Note that you can avoid creating the intermediate column using numpy.lexsort:

import numpy as np

out = df.iloc[np.lexsort([df['col2'],
                          df.groupby(['col1', 'col2']).cumcount(),
                          df['col1']])]

Output:

   col1  col2 col3
0     a     1    r
2     a     2    t
4     a     3    v
1     a     1    s
3     a     2    u
5     a     3    w
6     b     4    x
8     b     5    z
10    b     6    w
7     b     4    y
9     b     5    q
11    b     6    e

Intermediate (before sorting):

   col1  col2 col3  key
0     a     1    r    0
1     a     1    s    1
2     a     2    t    0
3     a     2    u    1
4     a     3    v    0
5     a     3    w    1
6     b     4    x    0
7     b     4    y    1
8     b     5    z    0
9     b     5    q    1
10    b     6    w    0
11    b     6    e    1