很巨挑戰性的 electrostatics

In cylindrical coordinate, from θ= 0 to θ= 2π/3 (r : 0 ->∞ , z : -∞ -> ∞) , the space is empty except there is a point charge Q, positioned at r = a, θ= π/3, z=0

for θ= 2π/3 to θ= 2π (r : 0 ->∞ , z : -∞ -> ∞) , the space is filled with perfect conductor

Find, the electric potential all over the space