- The curve \(C\), with pole \(O\), has polar equation
$$r = 1 + \cos \theta , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 2 }$$
At the point \(A\) on \(C\), the tangent to \(C\) is parallel to the initial line.
- Find the polar coordinates of \(A\).
- Find the finite area enclosed by the initial line, the line \(O A\) and the curve \(C\), giving your answer in the form \(a \pi + b \sqrt { 3 }\), where \(a\) and \(b\) are rational constants to be found.