8 The diagram shows a sketch of a curve \(C\) and a line \(L\), which is parallel to the initial line and touches the curve at the points \(P\) and \(Q\).
\includegraphics[max width=\textwidth, alt={}, center]{32de7ef6-b7aa-4bfd-a73a-e12bfc0147e2-5_506_762_447_639} The polar equation of the curve \(C\) is $$r = 4 ( 1 - \sin \theta ) , \quad 0 \leqslant \theta < 2 \pi$$ and the polar equation of the line \(L\) is $$r \sin \theta = 1$$

1. Show that the polar coordinates of \(P\) are \(\left( 2 , \frac { \pi } { 6 } \right)\) and find the polar coordinates of \(Q\).
2. Find the area of the shaded region \(R\) bounded by the line \(L\) and the curve \(C\). Give your answer in the form \(m \sqrt { 3 } + n \pi\), where \(m\) and \(n\) are integers.