Question 3 - A-Level Maths

Use de Moivre's theorem to show that $$\cos 4 \theta = \cos ^ { 4 } \theta - 6 \cos ^ { 2 } \theta \sin ^ { 2 } \theta + \sin ^ { 4 } \theta$$
Hence find all the roots of the equation $$x ^ { 4 } - 6 x ^ { 2 } + 1 = 0$$ in the form $\tan q \pi$, where $q$ is a positive rational number.