How to trust someone who lied about with another guy?

My girlfriend and I have been in a long distance relationship for the past 2 1/2 years. Recently we had our first break up and I flew across the world to patch things up. I dropped everything in my career and my education for several weeks just to fix things with her. While i was there, she was very distant from me and she talked to me very harshly and said little unloving remarks to me. After several lies and her denying it, I found out that she had had with someone else whilst i was there. obviously this crushed me severely bcos i had sacrificed sooo much to be there. My question is, am i supposed to accept being treated this way just because we were broken up during that 1 month period and now that we are back together in a long distance relationship, how do I trust her? how do i get over what happened? i want the future to be much better but i dont know the right words to say to let her know that i'm angry and hurt and want to be able to get over it and go back to loving her.?