Surface Integrals, Stokes & Divergence · Challenge problem

Find the area of the part of the unit sphere $x^2 + y^2 + z^2 = 1$ that lies inside the cube $|x| \le \dfrac{1}{\sqrt2}$, $|y| \le \dfrac{1}{\sqrt2}$, $|z| \le \dfrac{1}{\sqrt2}$. Give an exact answer.