2. The curve \(C\) has polar equation $$r = 1 + 2 \cos \theta , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 2 }$$ At the point \(P\) on \(C\), the tangent to \(C\) is parallel to the initial line.
Given that \(O\) is the pole, find the exact length of the line \(O P\).