(a)[3]
Express $5\sqrt{3}\cos x + 5\sin x$ as $R\cos(x - \alpha)$, where $R > 0$ and $0 < \alpha < \frac{1}{2}\pi$.
(b)[3]
As $x$ changes, find the least possible value of $4 + 5\sqrt{3}\cos x + 5\sin x$, and determine the matching value of $x$ for $-\pi < x < \pi$.
(c)[3]
Find the value of $\displaystyle \int \frac{1}{(5\sqrt{3}\cos 3\theta + 5\sin 3\theta)^2}\, d\theta$.