I came across the following question in the Year 12 Extension 1 Cambridge textbook:
Let $\theta_1$, $\theta_2$, $\theta_3$ and $\theta_4$ be the solutions of the equation $a\cos4\theta + b\sin4\theta=c$ such that $\tan\theta_1$, $\tan\theta_2$, $\tan\theta_3$ and $\tan\theta_4$ are distinct. Use the product of the roots of a quartic equation to prove that $\tan\theta_1\tan\theta_2\tan\theta_3\tan\theta_4=1$.
Honestly speaking, I have no idea how to even get started on this question here so any direction would be deeply appreciated!