What is the smallest integer $n\ge 4$ such that there exist distinct complex numbers $z_1,z_2,\dots ,z_n$ satisfying $|z_1|=|z_2|=\cdots =|z_n|=1$ and $z_1+z_2+\cdots +z_n=0$, but $z_1,z_2,\dots ,z_n$ are not equally spaced on the unit circle?