Need to take limit of divergence in spherical coordinates on the $\theta=0$ axis

Question

The title pretty much says it all. I need to take the standard expression (one of the standard expressions, I guess) for the divergence of a vector and of a rank-2 tensor in spherical coordinates and find the correct limits at $\theta\rightarrow 0$. It is clear to me that there are a couple of infinities that exactly cancel at this limit, and there are at least a few places where L'Hopital's rule comes into play, but keeping track of all the $O(\theta)$ terms is making my eyes cross. Does anyone know of somewhere where this has already been done?