The curve C has polar equation \(r = \frac{1}{\pi - \theta} - \frac{1}{\pi}\), where \(0 \leq \theta \leq \frac{1}{2}\pi\).

(a) Sketch C.

(b) Show that the area of the region bounded by the half-line \(\theta = \frac{1}{2}\pi\) and C is \(\frac{3 - 4 \ln 2}{4\pi}\).