(a)[6]
Show that the equation $\frac{1}{\cos \theta} + 3 \sin \theta \tan \theta + 4 = 0$ can be rewritten as $3 \cos^2 \theta - 4 \cos \theta - 4 = 0$, and hence solve the equation $\frac{1}{\cos \theta} + 3 \sin \theta \tan \theta + 4 = 0$ for $0^\circ \leq \theta \leq 360^\circ$.
(b)[2]
The diagram displays part of the graph of $y = a \cos x - b$, with $a$ and $b$ as constants. The graph intersects the $x$-axis at $C(\cos^{-1} c, 0)$ and the $y$-axis at $D(0, d)$. Find $c$ and $d$ in terms of $a$ and $b$.