(a)[3]
Show that the equation $\tan^3 x + 2\tan 2x - \tan x = 0$ can be rewritten as $\tan^4 x - 2\tan^2 x - 3 = 0$ for $\tan x \neq 0$.
(b)[3]
Hence solve the equation $\tan^3 2\theta + 2\tan 4\theta - \tan 2\theta = 0$ for $0 < \theta < \pi$. Write your answers in exact form.