Trigo(evaluate)

akki ~~ unlucky forever ~~

by doing rearrangement we have ,

$E=(tan^2\frac{\pi}{16}+cot^2\frac{\pi}{16}+2)+(tan^2\frac{2\pi}{16}+cot^2\frac{2\pi}{16}+2)+(tan^2\frac{3\pi}{16}+cot^2\frac{3\pi}{16}+2$ ) $+tan^2\frac{\pi}{4}-6$

$E=(tan\frac{\pi}{16}+cot\frac{\pi}{16})^2+(tan\frac{2\pi}{16}+cot\frac{2\pi}{16})^2+(tan\frac{3\pi}{16}+cot\frac{3\pi}{16})^2-5$

$E = \frac{4}{sin^2\frac{\pi}{8}}+\frac{4}{sin^2\frac{3\pi}{8}}+\frac{4}{sin^2\frac{\pi}{4}}-5$

$E=3+\frac{16}{sin^2\frac{\pi}{4}} = 35$