Let $y=y(x)$ be the solution of $x\tan(y/x)\,dy = (y\tan(y/x) - x)\,dx$, $-1\le x\le 1$, $y(1/2)=\pi/6$. Then the area of the region bounded by $x=0$, $x=1/\sqrt{2}$ and $y=y(x)$ in the upper half plane is