# Laplace equation between circles with Dirichlet boundary condition

I am wondering if the below problem is solvable or not. Laplace equation between two circle with raduses equal to $$r=1$$ and $$r=r_0$$ where $$r_0<1$$:

$$\nabla^2 \phi(r,\theta)=0$$

The boundary conditions are:

$$\phi(r=1,\theta)=\theta_1+\left\{ \begin{array}{ll} \pi/4 & 0<\theta<\pi \\ -\pi/4 & \pi<\theta<2\pi \end{array} \right.$$

$$\phi(r=r_0,\theta)=\theta_2+\left\{ \begin{array}{ll} -\pi/4 & 0<\theta<\pi \\ \pi/4 & \pi<\theta<2\pi \end{array} \right.$$

$$\theta_1$$ and $$\theta_2$$ are constants.