Question 9 - A-Level Maths

Use de Moivre's theorem to show that $$\sec 6 \theta = \frac { \sec ^ { 6 } \theta } { 32 - 48 \sec ^ { 2 } \theta + 18 \sec ^ { 4 } \theta - \sec ^ { 6 } \theta }$$
Hence obtain the roots of the equation $$3 x ^ { 6 } - 36 x ^ { 4 } + 96 x ^ { 2 } - 64 = 0$$ in the form sec $q \pi$, where $q$ is rational.