Problem

(a) It is given that $\beta$ is an angle between $90^\circ$ and $180^\circ$ such that $\sin\beta=a$.

Express $\tan^2\beta-3\sin\beta\cos\beta$ in terms of $a$.

(b) Solve the equation $\sin^2\theta+2\cos^2\theta=4\sin\theta+3$ for $0^\circ<\theta<360^\circ$.