(i)[3]
Show that $\cosec^2 \theta \equiv 2\cosec 2\theta \cot \theta$.
(ii)[2]
Hence show that $4 = \cosec^2 15^\circ \tan 15^\circ$.
(iii)[5]
Solve the equation $2\cosec \phi \cot \tfrac{1}{2}\phi + \cosec \tfrac{1}{2}\phi = 12$ for $-360^\circ < \phi < 360^\circ$. Include all necessary working.