Question 7 - A-Level Maths

Write down the formula for $\tan 2 x$ in terms of $\tan x$.
By letting $\tan x = t$, show that the equation $$4 \tan 2 x + 3 \cot x \sec ^ { 2 } x = 0$$ becomes $$3 t ^ { 4 } - 8 t ^ { 2 } - 3 = 0$$
Hence find all the solutions of the equation $$4 \tan 2 x + 3 \cot x \sec ^ { 2 } x = 0$$ which lie in the interval $0 \leqslant x \leqslant 2 \pi$.