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