Homework $6-$ Optional: Problem $43$

$(1$ point$)$

Let $F(x,y,z)=2z^2+(\frac{2}{3}{y}^3+tan(z))j+(2x^{2}z+5y^2)k.$ Use the Divergence Theorem to evaluate ${\displaystyle \underset{S}{\overset{\phantom{}}{}}}F*dS$ where $S$ is the top half of the sphere $x^2+y^2+z^2=1$ oriented upwards.

${}_{S}F*dS=$