Solution (source code)

= Solution

In <spherical coordinates>, the radial distance is $\sqrt{x^2+y^2+z^2}=\sqrt3$ and $\cos\theta=z/r$. Since the point lies below the equatorial <plane>, the polar angle exceeds $\pi/2$:
$$
\boxed{\theta=\arccos\left(-\frac1{\sqrt3}\right)}.
$$
The angle is approximately $2.1863$ radians, or $125.26^\circ$.