Show that the equation \(\tan ^ { 3 } x + 2 \tan 2 x - \tan x = 0\) may be expressed as
$$\tan ^ { 4 } x - 2 \tan ^ { 2 } x - 3 = 0$$
for \(\tan x \neq 0\).
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Hence solve the equation \(\tan ^ { 3 } 2 \theta + 2 \tan 4 \theta - \tan 2 \theta = 0\) for \(0 < \theta < \pi\). Give your answers in exact form.