(a)[3]
Express $6\sin\theta-4\cos\theta$ in the form $R\sin(\theta-\alpha)$, with $R>0$ and $0^\circ<\alpha<90^\circ$. Give the exact value of $R$ and state $\alpha$ correct to 2 decimal places.
(b)[4]
Hence solve $6\sin\theta-4\cos\theta+5=0$ for $0^\circ<\theta<360^\circ$.
(c)[3]
As $\beta$ changes, determine the greatest possible value of $(3\sin4\beta-2\cos4\beta)^2+15$ and the smallest positive value of $\beta$, in degrees, for which this greatest value occurs.