Gratuitously Polarized

$\begin{array} {cc} x = r \cos (\theta) \\ y=r \sin(\theta) \\ r = \sec(\theta) & \text{for } 0 \leq \theta \leq \frac{\pi}{4} \\ r = \csc(\theta)& \text{for } \frac{\pi}{4} < \theta \leq \frac{\pi}{2} \end{array}$

The curve described above exists within the $xy$ plane. Determine the area bounded by this curve, the $x$ -axis, and the $y$ -axis.