There are

*N* points which are randomly distributed (according to a uniform probability distribution) over the circumference of a circle.

Now consider the angular separation

between two neighbouring points. The sum of all these angular separations wil always correspond to one full rotation, i.e.:

The expected value of

can then be found as:

But the thing what I'm really dying to know is:

**how do I calculate the variance of** **? **
I've tried for several hours, but I just can't figure out where to start.

Does anyone here have any idea? Thanks in advance!