Get count of elements in a group in pandas data frame after group by but with date

Question

I have a data frame something like:

    id Col Col2    Date
    1   A   a   2022-10-03
    2   A   a   2022-10-03
    3   A   b   2022-10-03
    4   A   a   2022-10-04
    5   A   a   2022-10-04
    6   B   c   2022-10-03
    7   B   d   2022-10-03
    8   B   c   2022-10-03
    9   B   d   2022-10-04
    10  B   c   2022-10-04

and i want the count of every unique element in Col2 by date so basically my data frame should be looking like:

        id Col    Date       count
        1   A   2022-10-03    2
        2   A   2022-10-04    1  
        3   B   2022-10-03    2
        4   B   2022-10-04    2

Explaining it a little better: for Column Col2 for date 2022-10-03 we have 2 unique elements namely a and b. and for date 2022-10-04 we have the just one unique element which is a.

I am not able to think of any approach as such..I tried grouping by but i was not very successful. If anybody can help it will be really appreciated. Thank you.