Use de Moivre's theorem to show that
\(\sin 5 \theta=16 \sin ^{5} \theta-20 \sin ^{3} \theta+5 \sin \theta .\)

Hence find all the roots of the equation
\(32 x^{5}-40 x^{3}+10 x+1=0\)
in the form \(\sin (q \pi)\), where \(q\) is a positive rational number.