(i)[3]
Show that $2\cosec^2 2x(1-\cos 2x)\equiv \sec^2 x$.
(ii)[4]
Solve the equation $2\cosec^2 2x(1-\cos 2x)=\tan x+21$ for $0<x<\pi$, giving your answers correct to $3$ significant figures.
(iii)[3]
Find $\int \left[2\cosec^2(4y + 2) - 2\cosec^2(4y + 2)\cos(4y + 2)\right] \, dy$.