In this post, I am unsure which angles are denoted in general equation of quantum state.
I realize that $\theta$ is azimuthal angle, while $\phi$ is the polar angle. Some textbooks treat it reverse way.
Try to visualise it: $|0\rangle$ is at the north pole of the sphere, and $|1\rangle$ is at the south pole. You get between them by varying the angle $\theta$ from 0 to $\pi$.
$\phi$ then defines an angle around the equator. Since it can be anywhere around the equator, it goes from 0 to $2\pi$. If you've got your visualisation correct, you should be able to confirm that there's no double-counting of positions on the surface of the sphere.
