Find an exact triangle area from an implicit normal

Example 11 (Self-Reading): The curve $C$ has equation $\sin(x+y)=\sin x+\cos y$. Its normal at $P(\pi/4,\pi/2)$ meets the x- and y-axes at $S$ and $T$ respectively. Find the exact area of triangle $OST$, where $O$ is the origin, in the form $\dfrac{\pi^2}{64}(a+b\sqrt c)$, where $a,b,c$ are positive integers to be determined.7 marks