Let \(y=y(x)\) be the solution of the differential equation \(x\tan \left(\frac{y}{x}\right)dy=\left(y\tan \left(\frac{y…

Let \(y=y(x)\) be the solution of the differential equation

\(x\tan \left(\frac{y}{x}\right)dy=\left(y\tan \left(\frac{y}{x}\right)-x\right)dx,-1\leq x\leq 1,y\left(\frac{1}{2}\right)=\frac{\pi }{6}\)

Then the area of the region bounded by the curves \(x=0,x=\frac{1}{\sqrt{2}}\) and \(y=y(x)\) in the upper half plane is :

[JEE Main 2021, 20 Jul (Shift 1)]