Attachment 26019

I started by trying to solve for G for x and H for y, so that we could proceed to the Jacobian. However

it lead to this mess X=cot^-1(2/H) but then I'm left with Y=(H/sin(X))^2/2 (here clearly I don't want an X in the RHS). So I'm stuck. Is there a better way to go about this?