Trigonometry - Trigonometric Equations

Prove the identity \(\operatorname{cosec} 2x (1 - \cos 2x) = \tan x\).

Hence solve the equation \(\operatorname{cosec} 4\theta (\cos 4\theta - 1) = 3 \tan^2 \left( \frac{\pi}{2} - 2\theta \right)\), for \(0 \le \theta \le 2\).