(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 $\cosec \theta (3 \sin 2\theta + 4 \sin^3 \theta) + 3 = 0$ in the interval $-\pi < \theta < 0$.
(c)[3]
Find the value of $\int \cosec \theta (3 \sin 2\theta + 4 \sin^3 \theta) \, d\theta$.