(a)[3]
Show that $\cosec\theta(3\sin 2\theta + 4\sin^3 \theta)$ is equal to $4 + 6\cos \theta - 4\cos^2 \theta$.
(b)[3]
Solve the equation $\cosec\theta(3\sin 2\theta + 4\sin^3 \theta) + 3 = 0$ for $-\pi < \theta < 0$.
(c)[3]
Find the integral $\int \cosec\theta(3\sin 2\theta + 4\sin^3 \theta)\, d\theta$.