Continuous model of geographic direction (e.g. as ML predictor)

Question

Imagine the geographical direction from N, over NNE, NE, E ,... and so on. They are also represented from 0 to 360 degrees.

So far so easy.

Now I want to use the arc degree as a predictor in a machine learning model.

The problem is the break between 360 and 1 degrees, which is physically similar, but not numeric.

Ideas how to avoid this break?