(i)[3]
Express $8\cos\theta + 15\sin\theta$ in the form $R\cos(\theta - \alpha)$, where $R > 0$ and $0^\circ < \alpha < 90^\circ$. State $\alpha$ correct to 2 decimal places.
(ii)[4]
Hence, solve the equation $8\cos\theta + 15\sin\theta = 12$, giving every solution in the interval $0^\circ < \theta < 360^\circ$.