(i)[3]
Write $3\cos \theta + \sin \theta$ as $R\cos(\theta - \alpha)$, 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]
Therefore solve $3\cos 2x + \sin 2x = 2$, listing all solutions in the interval $0^\circ \leq x \leq 360^\circ$.