Outline proof: For , let denote the angle . The points are equally spaced around the unit circle, so their centre of mass is at the origin, and it follows that

Since and , it follows that

Next,

.

But (with similar results for and ). Also, (with similar results for the other two products and ).

Putting all that together, you find that

, and

Now let and It follows from the above calculations that and Eliminate T between those equations to get , a quadratic with solutions Now all that remains for you to do is to figure out why the square root must have the plus sign.