Automatically find and display overlapping time slots

If there’s a working solution for this, please point me to it.

Assume that multiple team members want an easy way to find a suitable day/time for a weekly recurring meeting.
And assume each member marks certain weekdays and times in their calendar that would work well for that person (for a weekly meetup).
Also, assume that these people are across different time zones.

Now, ideally, we want the app to automatically display:
which days and times (expressed in each person’s own time zone)
would work for everyone for these weekly meetings.

That way, all team members could immediately see
Tuesdays 10:30 am would work for everyone (as an example).

How can this be done?
Are there working examples or templates for this?
Or are there third-party APIs that could be used for this?

This is a complicated problem. I have done a view of Apps with a similar problem… lots of work, especially with multiple connected calendars.