Find a conformal transformation $\zeta=\zeta(z)$ that maps the domain $D, 0<\arg z<\frac{3 \pi}{2}$, on to the strip $0<\operatorname{Im}(\zeta)<1$.

Hence find a bounded harmonic function $\phi$ on $D$ subject to the boundary conditions $\phi=0, A$ on $\arg z=0, \frac{3 \pi}{2}$, respectively, where $A$ is a real constant.