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...I was looking for something, and it took some time to find it:

 
If there are two directions/vectors, I was aware that the scalar/dot product can tell me something about the angle between, and the pocket calculator proudly advertised me then the ArcCos function to turn it into a radian or a degree.
Too bad now that DS2 doesn't support ArcCos, but amazingly the game knows to ArcTan ...!

I had no concrete idea about that formula above, but I remembered that there are hair-raising expressions to transfrom one trigonometrical term into another, so I started to check some sites to find a substitute or at least an approximation.