Direction to an actor, relative to players orientation

Hi, this may be a stupid question, but I can’t figure it out by myself.
I need to know, how I can find the direction to an actor, relatively to the players own rotation.
In my case, I want to use this to draw the direction to objects on a compass.

Finding the absolute direction is a piece of cake: atan2(y,x) is doing the job.
Making it relative to the players rotation is just as easy: [direction to actor] - [rotation of player]

But: When my players rotation switches from 180° to -180°, the relative direction switches, too. Of course, it does.
And on my compass the objects seem to jump to a different position, which is really annoying.

Does anyone have an idea, how to get the direction to an actor, relatively to the own orientation?
There may be a ready-to-use-function, that I simply don’t know?