I know the general method for this question, but I'm struggling with finding limits on $\displaystyle \theta$ and $\displaystyle \phi$

Calculate the area of the portion $\displaystyle E_+$ of the ellipsoid $\displaystyle \frac{x^2}{4}+\frac{y^2}{4}+z^2=1$ that lies above the xy plane by making use of the parameterisation $\displaystyle r(\theta,\phi) = (2\cos{\phi}\sin{\theta},2\sin{\phi}\sin{\theta},\ cos{\theta})$

What I've got is that because it lies above the xy plane, we have $\displaystyle z\geq0$ so $\displaystyle cos{\theta}\geq0 \implies 0\leq\theta\leq\frac{\pi}{2} $

I don't think there is any restriction on $\displaystyle \phi$ so we have $\displaystyle 0\leq\phi\leq2\pi$

?