Steady temperature in a sphere with hemispheres at different temperatures

The surface of a sphere of radius R is kept at a constant temperature \(T _ { U }\) for the upper hemisphere \(( 0 \leq \theta < \pi / 2 )\) and \(T _ { L }\) for the lower hempisphere \(( \pi / 2 \leq \theta \leq \pi )\) . Find the stationary temperature distribution inside the sphere, at a distance r from the center, in an expansion in terms of \(\frac { r } { R }\) . Compute terms up to third order.