(i)[3]
Express $\sin 2\theta (3\sec \theta + 4\cosec \theta)$ as $a \sin \theta + b \cos \theta$, with $a$ and $b$ integers.
(ii)[3]
Hence write $\sin 2\theta (3\sec \theta + 4\cosec \theta)$ in the form $R \sin(\theta + \alpha)$, where $R > 0$ and $0^\circ < \alpha < 90^\circ$.
(iii)[4]
Using the result from part (ii), solve the equation $\sin 2\theta (3\sec \theta + 4\cosec \theta) = 7$ for $0^\circ \leq \theta \leq 360^\circ$.