4 The equation of a curve, in polar coordinates, is
$$r = 2 \cos 2 \theta \quad ( - \pi < \theta \leqslant \pi ) .$$
- Find the values of \(\theta\) which give the directions of the tangents at the pole.
One loop of the curve is shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{e4e1c424-8dd5-4d18-9950-e902de0301b0-3_362_720_653_708} - Find the exact value of the area of the region enclosed by the loop.