(a)[5]
Solve the equation $3\sin^2 2\theta + 8\cos 2\theta = 0$ for $0^\circ \leq \theta \leq 180^\circ$.
(b)[3]
The diagram shows part of the curve $y = a + \tan bx$, with $x$ measured in radians and $a$ and $b$ as constants. The curve cuts the $x$-axis at $\left(-\frac{pi}{6}, 0\right)$ and the $y$-axis at $(0, \sqrt{3})$. Determine the values of $a$ and $b$.