Plotting regions in complex plane

Question

Plot the region represented by $\frac{π}{3}\leqslant \arg\left(\frac{z+1}{z-1}\right)\leqslant\frac{2π}{3}$ in the Argand plane.

I know that such inequalities usually represent the minor or major arcs of the circle and the area bounded by them,but I can't figure out this one. Any help is appreciated.

Answer 1

Hint: Think of all arcs like $$\arg\left(\frac{z+1}{z-1}\right)=\theta$$but keeping $\theta$ in the given range.

Please ask if you need more details.

Edit: Adding Desmos graph