How to treat somebody who is a cheater?

Anonymous
so my LDR girlfriend went to spain for a few months due to work. A few weeks ago while talking on the phone she told me that a handsome guy at the park approached her and start talking to her. she also mentioned me she talked to him back because she didn't want to seem disrespectful. Also she said he is a teacher and a historian. i asked her why would you tell me this to make me jealous? and i made a joke asking her if she gave him her number which she said ofc not i would never do that!. i didn't pay much attention and i thought that she did it to make me jealous. After some time from that incident she start becoming distant to me out of nowhere, less talking, weak conversations.. i suspected that something is going wrong and i asked her if she is talking with someone, right away she became defensive and started crying saying am a sick person thinking like that and some other accusations. recently i was checking her instagram "on purpose" and i saw somebody who liked one of her pictures matched the description she told me when we were talking on the phone weeks earlier. (historian, teacher, blue eyes). when i saw they followed each other i completely lost it and i texted her. I need to mention that i already knew his name from IG. so i asked her " what was the name of that teacher guy you mentioned me a few weeks ago? and she was like " "why you ask?" and she proceed and told me a complete different name!! so i proceed and i told her his real name! also i ask her if she has something to tell me? she called me right away and start attacking me that i am a sick person that i search her personal things and am immature , and start accusing me about some things that happened in the past and that i am the one who i might cheat. later she start crying saying she is in a bad situation and blah blah blah. eventually she hung up the phone. its been 2 days after the incident and there is no communication whatsoever. how should i end things?
How to treat somebody who is a cheater?
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