(a)[6]
Express $4 \sin \theta \sin (\theta + 60^\circ)$ as $a + R \sin (2\theta - \alpha)$, where $a$ and $R$ are positive integers and $0^\circ < \alpha < 90^\circ$.
(b)[3]
Hence determine the smallest positive value of $\theta$ that satisfies the equation $\frac{1}{5} + 4 \sin \theta \sin (\theta + 60^\circ) = 0$.