transforming from spherical coordinates

This question is born from a question relating to Stokes' theorem, where I'm evaluating the surface integral.

The area I'm confused with is where I need to transform the follwing into speherical polar coordinates:

$\displaystyle

\int\int_{S} (\nabla \times F)\cdot \bold{\hat{n}}\ dS \ = \frac{1}{2}\int\int_S(-yz-3z)\ dS$

where

$\displaystyle x=2\cos\phi\sin\theta\ y=2\sin\phi\sin\theta\ z=2\cos\theta$

how would I transform the above integral into one wrt $\displaystyle d\theta\ d\phi$?