Ok so about ten months ago my girlfriends parents made us break up, they took her phone internet and every other way she had of talking to me. and by the time her parents allowed her to date again she had found another man. anyway. she still has that man, but i can tell she doesnt like him anymore. he is too clingy and she never responds to him on facebook. also she found out that i cheated on her when we were together, i tried to appologize a few months ago but she took it very seriously and was very hateful towards me. how should i re initiate contact with this girl? i kinda want her back. what should i message her on facebook?

Not only is that relationship a pain in the ass because of the parent's behavior, you also fucked it up by cheating on another girl AND she already is seeing another guy.

Do you want to waste your time?

Face consequences of your behavior and leave the girl alone. You acted immature: learn from your mistakes, go out again, look for new girls and forget about this one.

This. Not only you're wasting your time, you'll also be wasting her time.

Leave her alone. Pick up other women, maybe you'll meet in the future.