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