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\includegraphics[max width=\textwidth, alt={}, center]{1b410c91-2fe9-46cf-8478-631b4165f98d-12_424_488_260_826} The diagram shows the curve with equation \(y = \sin 2 x + 3 \cos 2 x\) for \(0 \leqslant x \leqslant \pi\). At the points \(P\) and \(Q\) on the curve, the gradient of the curve is 3 .

1. Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
2. By first expressing \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in the form \(R \cos ( 2 x + \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\), find the \(x\)-coordinates of \(P\) and \(Q\), giving your answers correct to 4 significant figures.
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