(a)[3]
It is given that $\beta$ is an angle between $90^\circ$ and $180^\circ$ for which $\sin \beta = a$. Express $\tan^2 \beta - 3 \sin \beta \cos \beta$ in terms of $a$.
(b)[5]
Solve the equation $\sin^2 \theta + 2 \cos^2 \theta = 4 \sin \theta + 3$ for $0^\circ < \theta < 360^\circ$.