Use de Moivre's theorem to show that
\(\tan 5 \theta=\frac{5 t-10 t^{3}+t^{5}}{1-10 t^{2}+5 t^{4}}\)
where \(t=\tan \theta\).

Deduce that the roots of the equation \(t^{4}-10 t^{2}+5=0\) are \(\pm \tan \frac{1}{5} \pi\) and \(\pm \tan \frac{2}{5} \pi\).

Hence show that \(\tan \frac{1}{5} \pi \tan \frac{2}{5} \pi=\sqrt{ } 5\).