If getting your ex back is still on your mind then here are the things you should do:
First of all, if it's not you who caused the break-up then don't take the blame for it. You must be able to make your ex realize that it's not your fault in the first place. It was your ex who played around and not you, so why blame it all on you? If your ex really deserves to have you back, then your ex must be able to come to terms with accepting that it is his/her fault and not yours. Make them accept it, if they simply can't then just forget about her or him. It means that they do not deserve you at all.
Secondly, you must be able to figure out what really happened between the two of you. Or what is the real reason behind your break-up. Is it a third party? Or plainly someone fell out of love. If the reason is a third party, then it is all clear that things are not really going great between the two of you. And if someone fell out of love during your relationship, then it is not a good sign at all. So why try to win someone back and go crazy over that person when the love is gone? It's pointless! If you think that it is worth reviving (the relationship), then go ahead do whatever you can and try your best and hope that there is an actual chance in getting your ex back.
Being able to admit mistakes is something that is not that easy to do. What more if it is something that caused you and your ex to part ways. But taking the blame for something that you did not do is not right as well. it sounds pathetic. That person does not deserve you at all. Let that person be the one to want to have you back since it's their fault in the first place.