(a(i))[3]
Rewrite $5\sin 2\theta + 2\cos 2\theta$ as $R\sin(2\theta + \alpha)$, where $R > 0$ and $0^\circ < \alpha < 90^\circ$, and give the exact value of $R$ together with $\alpha$ correct to $2$ decimal places.
(a(ii))[5]
Hence solve $5\sin 2\theta + 2\cos 2\theta = 4$, giving every solution in the interval $0^\circ \le \theta \le 360^\circ$.
(a(iii))[2]
Find the least value of $\displaystyle \frac{1}{(10\sin 2\theta + 4\cos 2\theta)^2}$ as $\theta$ changes.