5 The curve \(C\) has polar equation \(r ^ { 2 } = \frac { 1 } { \theta ^ { 2 } + 1 }\), for \(0 \leqslant \theta \leqslant \pi\).
- Sketch \(C\) and state the polar coordinates of the point of \(C\) furthest from the pole.
- Find the area of the region enclosed by \(C\), the initial line, and the half-line \(\theta = \pi\).
- Show that, at the point of \(C\) furthest from the initial line,
$$\left( \theta + \frac { 1 } { \theta } \right) \cot \theta - 1 = 0$$
and verify that this equation has a root between 1.1 and 1.2.