MDX Between Start Date and End Date

How do you use MDX to find the number of items between two dates, when the start date and end date are different role playing dimensions?

I had an interesting question from Ricardo Santos on another frog-blog post this week (MDX Calculated Member spanning multiple date dimensions). I answered Ricardo in the post, but it was a good question which I thought deserved a full blog post on its own. So thanks to Ricardo for prompting this.