I read some notes on Laplace. I ran into a short answer question as follows.
We have a Laplace equation in Polar Systems:
$\frac{1}{r}\frac{\partial}{\partial r}(r\frac{\partial u}{\partial r})+\frac{1}{r^2}\frac{\partial^2u}{\partial \theta^2} $
with boundary conditions:
$u(a,\theta)=\begin{cases}2\theta & 0<\theta<\pi\\0 & \pi<\theta<2\pi\end{cases}$
then the value of $U(0, \theta)=\pi$.
My Challenge is How this value will be reached? I found $U(0, \theta)=2\pi$. Any Ideas?