(a)[3]
Find the possible values of $x$ satisfying $\sin^{-1}(x^2 - 1) = \frac{1}{3}\pi$, and give each answer correct to $3$ decimal places.
(b)[4]
Solve $\sin\left(2\theta + \frac{1}{3}\pi\right) = \frac{1}{2}$ for $0 \leq \theta \leq \pi$, and express your answers for $\theta$ in terms of $\pi$.