(i)[3]
Express $5\sin 2\theta + 2\cos 2\theta$ in the form $R\sin(2\theta + \alpha)$, where $R > 0$ and $0^\circ < \alpha < 90^\circ$, and give the exact value of $R$ as well as the value of $\alpha$ correct to $2$ decimal places.
(ii)[5]
Hence solve the equation $5\sin 2\theta + 2\cos 2\theta = 4$, giving every solution in the interval $0^\circ \leq \\theta \\leq 360^\circ$.
(iii)[2]
Determine the least possible value of $\displaystyle \frac{1}{(10\sin 2\theta + 4\cos 2\theta)^2}$ as $\theta$ varies.