(i) Use de Moivre's theorem to show that
\(\sin 8 \theta=8 \sin \theta \cos \theta\left(1-10 \sin ^{2} \theta+24 \sin ^{4} \theta-16 \sin ^{6} \theta\right)\).

moniainatian
(ii) Use the equation \(\frac{\sin 8 \theta}{\sin 2 \theta}=0\) to find the roots of
\(16 x^{6}-24 x^{4}+10 x^{2}-1=0\)
in the form \(\sin k \pi\), where \(k\) is rational.