5 The curve \(C\) has polar equation \(r = \frac { 1 } { \pi - \theta } - \frac { 1 } { \pi }\), where \(0 \leqslant \theta \leqslant \frac { 1 } { 2 } \pi\).
- Sketch \(C\).
- Show that the area of the region bounded by the half-line \(\theta = \frac { 1 } { 2 } \pi\) and \(C\) is \(\frac { 3 - 4 \ln 2 } { 4 \pi }\).