I have three random points in a 2D space, $A$, $B$ and $C$, how can I compute the angle between the abscisse and the bisector of $ABC$:
So I am looking for the angle $α$ (in red).
I'm using a computer and I can easily compute the azimuth $AZIMUTH_{BA}$ and $AZIMUTH_{BC}$
For this specific example I can do:
$$\frac{AZIMUTH_{BA}-AZIMUTH_{BA}}{2} + \frac{5\pi}{2} - AZIMUTH_{BA}$$
To get the angle $α$.
But how can I get a generalized formula to always get the right $α$ angle between $0$ and $2\pi$ ?