(a)[6]
Express $3\sin 2\theta \sec \theta + 10\cos(\theta - 30^\circ)$ in the form $R\sin(\theta + \alpha)$ where $R > 0$ and $0^\circ < \alpha < 90^\circ$. Give the value of $\alpha$ correct to 2 decimal places.
(b)[3]
Hence, solve the equation $3\sin 4\beta \sec 2\beta + 10\cos(2\beta - 30^\circ) = 2$ for $0^\circ < \beta < 90^\circ$.