[AccessD] Strange date question

I have a beginning date and an ending date in my events table.  I need to
find out how many days in any given month that one or more events happened.
For example,
Event 1  Beginning Date 1/3/05   Ending date 1/3/05
Event 2  Beginning Date 1/3/05   Ending date 1/4/05
Event 3  Beginning Date 1/3/05   Ending date 1/8/05
Event 4  Beginning Date 1/6/05   Ending date 1/7/05
Event 5  Beginning Date 1/10/05 Ending Date 1/11/05

My query, function, module, whatever works needs to tell me:
between 1/1/05 and 1/11/05 events happened on 6 days.
I can not figure out how to disinclude events if they happened within the
beginning and ending date of other events.