Evaluate $\displaystyle \oint_{C}(y^3+cosx)dx+(siny+z^2)dy+xdz$, where C is the closed curve parameterized and oriented by the path $\displaystyle \vec{x}(t)=(cost,sint,sin2t)$.

Hint: Show that the path $\displaystyle \vec{x}(t)$ lies on the surface $\displaystyle z=2xy$.