(a) Use de Moivre's theorem to show that
\(\sec 5 \theta=\frac{\sec ^{5} \theta}{5 \sec ^{4} \theta-20 \sec ^{2} \theta+16} .\)
(b) Hence, obtain the roots of the equation
\(\sqrt{3} x^{5}-10 x^{4}+40 x^{2}-32=0\)
in the form \(\sec (q \pi)\), where \(q\) is rational.