%V0
Prove the identity
$\sum\limits_{k=0}^n\binom{n}{k}\left(\tan\frac{x}{2}\right)^{2k}\left(1+\frac{2^k}{\left(1-\tan^2\frac{x}{2}\right)^k}\right)...$
for any natural number $n$ and any angle $x.$
Izvor: Međunarodna matematička olimpijada, shortlist 1967
Školjka 
and any angle 