(i)[3]
Express $3\cos\theta + \sin\theta$ in the form $R\cos(\theta - \alpha)$, where $R > 0$ and $0^\circ < \alpha < 90^\circ$, and state the exact value of $R$ together with the value of $\alpha$ correct to $2$ decimal places.
(ii)[5]
Hence solve the equation $3\cos 2x + \sin 2x = 2$, and list all solutions in the interval $0^\circ \leq x \leq 360^\circ$.