Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
To prove $ \tan(A) + 2 \tan(2A) +4\tan4A + 8 \cot8A =\cot(A) $