Hi !
(I know a proof, so it's like a challenge question)
Prove that , where and
See this blog post of mine from last February for a proof of this, as a corrolary of a geometric proof using complex numbers.
--Kevin C.
I posted a proof a long time ago here.
Another interesting one (from number theory) is if then:
(I do not think this is solvable by ordinary trigonometry techinques it is a special result from number theory).
It generalizes to when is any positive integer integer.