(a) Use de Moivre's theorem to show that
\(\operatorname{cosec} 5 \theta=\frac{\operatorname{cosec}^{5} \theta}{5 \operatorname{cosec}^{4} \theta-20 \operatorname{cosec}^{2} \theta+16} .\)
(b) Hence obtain the roots of the equation
\(x^{5}-10 x^{4}+40 x^{2}-32=0\)
in the form \(\operatorname{cosec}(q \pi)\), where \(q\) is rational.