Construct a harmonic function $u(z)$ in the disc $|z|<R$ for which $\lim_{r\to R} u( r e^{i\theta} )= 0$ if $ 0< \theta <\pi $ and $1$ if $\pi < \theta < 2 \pi$.
This question is from my complex analysis mid term and I couldn't solve it and so I am asking for guidance here.
I don't have much problem solving experience in harmonic functions and I don't even have a clue on how this question should be approached. So, I am looking for a solution here.