How can I solve this PDE?

I got the following equation from physics.

$ $ C \sin \theta \frac{\partial T}{\partial \theta} = \frac{1}{r} \frac{\partial }{\partial r} \left( r \frac{\partial T}{\partial r} \right)$ $ where boundary conditions are

$ T=T_w$ for $ r<r_0$ ,

$ T=T_0$ where $ r \rightarrow\infty$ ,

and $ C, T_0, T_w, r_0$ are constant.

(Symmetrical for all $ \theta$ )

I would like to find $ \frac{\partial T}{\partial r}$ where $ r=r_0$ from the equation.

How can I solve using Mathematica? Thank you so much!