(i)[3]
If $\sec \theta + 2\cosec \theta = 3\cosec 2\theta$, prove that $2\sin \theta + 4\cos \theta = 3$.
(ii)[3]
Write $2\sin \theta + 4\cos \theta$ in the form $R\sin(\theta + \alpha)$ with $R > 0$ and $0^\circ < \alpha < 90^\circ$, and give $\alpha$ correct to $2$ decimal places.
(iii)[4]
Hence solve $\sec \theta + 2\cosec \theta = 3\cosec 2\theta$ for $0^\circ < \theta < 360^\circ$.