Show that $$\int\limits_{0}^{2\pi} \int\limits_{0}^{\pi} \frac{u_{\phi \phi}}{\sin\theta} d\theta\,d\phi = 0 $$ Where $u$ is a function of $\theta$ and $\phi$.
I am unable to show that this integral is in fact $0$. This is because the of the $\frac{1}{\sin\phi}$, which ultimately yields undefined values over that interval for $\phi$.
Is it possible to show that this integral is undefined or is it really $0$?