Solution
= Solution
The angular Laplacian sends $\sin\theta$ to $\cos(2\theta)/\sin\theta$, while $1/r$ is radially harmonic. Therefore
$$
\boxed{u=\frac{\sin\theta}{r}.}
$$
= Solution
The angular Laplacian sends $\sin\theta$ to $\cos(2\theta)/\sin\theta$, while $1/r$ is radially harmonic. Therefore
$$
\boxed{u=\frac{\sin\theta}{r}.}
$$