Use de Moivre's theorem to show that
\(\cos 5 \theta \equiv \cos \theta\left(16 \sin ^{4} \theta-12 \sin ^{2} \theta+1\right)\)

By considering the equation \(\cos 5 \theta=0\), show that the exact value of \(\sin ^{2}\left(\frac{1}{10} \pi\right)\) is \(\frac{3-\sqrt{ } 5}{8}\).