Use de Moivre's theorem to show that
$$\cos 4 \theta = 8 \cos ^ { 4 } \theta - 8 \cos ^ { 2 } \theta + 1$$
Hence obtain the real roots of the equation
$$16 \left( 8 x ^ { 4 } - 8 x ^ { 2 } + 1 \right) ^ { 4 } - 9 = 0$$
in the form \(\cos ( q \pi )\), where \(q\) is a rational number.