I have found that 羽目になる means: to get stuck with (some job); to end up with (something unpleasant)
But I cannot make sense of it for the following sentence
The context is of a veteran police inspector giving some advice to a new recruit on her first case.
あんたが教わってきた事柄は全て理詰めのセオリーだ それがどれだけ無意味なもんか すぐに思い知る羽目になるだろさ まあ覚悟だけはしておくんだな
Everything you've been taught is based on theories and logic. Soon, you'll likely come to realize how pointless they are. Well, at least be prepared.
Note: it is about the same sentence as one I used in another question (Specificity of the use of 事柄) , but for a different word