Let $\mathbf{F}(x,y,z)=2 z^2 x\mathbf{i} + (\frac {2} 3 y^3 + \tan(z))\mathbf{j} + (2 x^2z - 3 y^2)\mathbf{k}$. Use the Divergence Theorem to evaluate $\int_S \mathbf{F} \cdot \ d \mathbf{S}$ where $S$ is the top half of the sphere $x^2+y^2+z^2=1$ oriented upwards.

$\int\int_S \mathbf{F} \cdot \ d \mathbf{S}=$