Sketch the graph of \(y = \cos x\) in the interval \(0 \leqslant x \leqslant 2 \pi\). State the values of the intercepts with the coordinate axes.
Given that
$$\sin ^ { 2 } \theta = \cos \theta ( 2 - \cos \theta )$$
prove that \(\cos \theta = \frac { 1 } { 2 }\).
Hence solve the equation
$$\sin ^ { 2 } 2 x = \cos 2 x ( 2 - \cos 2 x )$$
in the interval \(0 \leqslant x \leqslant \pi\), giving your answers in radians to three significant figures.