(i)[3]
Starting from $3\sin^2 x - 8\cos x - 7 = 0$, show that, for real values of $x$, $\cos x = \frac{2}{3}$.
(ii)[4]
Hence find the solutions of $3\sin^2(\theta + 70^\circ) - 8\cos(\theta + 70^\circ) - 7 = 0$ for $0^\circ \leq \theta \leq 180^\circ$.