Answer
$\phi_0=0 $, $\phi_0=\pi $
Work Step by Step
In spherical coordinates, we have
$$
\begin{aligned}
&x=\rho \sin \phi \cos \theta\\
&y=\rho \sin \phi \sin \theta\\
&z=\rho \cos \phi
\end{aligned}
$$
When $\phi_0=0 $, we get $x=0,y=0, z=\rho$, which is a half-line.
When $\phi_0=\pi $, we get $x=0,y=0, z=-\rho$, which is a half-line.