The curves \(C_{1}\) and \(C_{2}\) have polar equations, for \(0 \leqslant \theta \leqslant \pi\), as follows:
\(\begin{array}{l}
C_{1}: r=a \\
C_{2}: r=2 a|\cos \theta|
\end{array}\)
where \(a\) is a positive constant. The curves intersect at the points \(P_{1}\) and \(P_{2}\).
(i) Find the polar coordinates of \(P_{1}\) and \(P_{2}\).

(ii) In a single diagram, sketch \(C_{1}, C_{2}\) and their line of symmetry.

(iii) The region \(R\) enclosed by \(C_{1}\) and \(C_{2}\) is bounded by the arcs \(O P_{1}, P_{1} P_{2}\) and \(P_{2} O\), where \(O\) is the pole. Find the area of \(R\), giving your answer in exact form.