I have a line segment given by two points $A$ and $B$, that are $(r_1,\theta_1)$ and $(r_2,\theta_2)$ in Polar coordinates.
I know that the direction angle of the line segment is given by:
$$\theta_0=\begin{cases} \tan^{-1}\left(\frac{y2-y1}{x2-x1}\right), & x_1\ne x_2 \\ \frac{\pi}2, & x_1=x_2 \end{cases} $$
where $(x_1,y_1)$ and $(x_2,y_2)$ are the points $A$ and $B$ in Cartesian coordinates.
Is there any way to get $\theta_0$ without converting to Cartesian coordinates?