How can I loop for end of month date between to dates in sh?

I want to loop and print end of month date between two dates.

I have below code but it prints day on day.

startdate='2021-01-01'
enddate='2021-04-01'

enddate=$( date -d "$enddate + 1 day" +%Y%m%d )   # rewrite in YYYYMMDD format
                                                  #  and take last iteration into account
thedate=$( date -d "$startdate" +%Y%m%d )
while [ "$thedate" != "$enddate" ]; do
    printf 'The date is "%s"n' "$thedate"
    thedate=$( date -d "$thedate + 1 days" +%Y%m%d ) # increment by one day
done

but I want these result for:

  startdate='2021-01-01'
    enddate='2021-04-01'

20210131

20210228

20210331

thanks in advance

Answer

Something like this

    year=$(date +%Y)
for month in {01..04}; {
    day=($(cal -d $year-$month))
    echo "$year$month${day[@]:(-1)}"
}
20210131
20210228
20210331
20210430

or with -m flag

year=$(date +%Y)
for month in {01..04}; {
    day=($(cal -m $month $year))
    echo "$year$month${day[@]:(-1)}"
}
20210131
20210228
20210331
20210430