Question 1
(BEL 3) Consider a regular $2n$-gon and the $n$ diagonals of it that pass through its center. Let $P$ be a point of the inscribed circle and let $a_1,a_2,\ldots,a_n$ be the angles in which the diagonals mentioned are visible from the point $P$. Prove that
$$\sum_{i=1}^n\tan^2a_i=2n\frac{\cos^2\frac{\pi}{2n}}{\sin^4\frac{\pi}{2n}}.$$
$$\sum_{i=1}^n\tan^2a_i=2n\frac{\cos^2\frac{\pi}{2n}}{\sin^4\frac{\pi}{2n}}.$$