(i)[3]
Write $\cos x + 3\sin x$ in the form $R\cos(x - \alpha)$, with $R > 0$ and $0^\circ < \alpha < 90^\circ$, and give the exact value of $R$ together with $\alpha$ correct to $2$ decimal places.
(ii)[5]
Hence find the solution(s) of $\cos 2\theta + 3\sin 2\theta = 2$, for $0^\circ < \theta < 90^\circ$.