Parametrize plane to calculate contour integrals and prove stoke’s theorem

Question

There is a vector field $G=\langle -zy^2/2, -xz^2/2, yx^2/2\rangle$ and a given plane $z=1-x-y$. I was given the curled vector field to use stokes theorem to calculate the surface integral. Basically now I have to use parametrization to deconstruct the plane and use the non curled vector field to calculate the contour integral and verify the answer which should be $1/2$. I’m not sure how to do this. Could I get some guidance please?