Do I break up with her?

So I work on a fishing boat and moved my girlfriend of 3 years to live with me in another state so when I'm on land we can be together. However a couple weeks ago she went to a rave with a friend of mine who supposedly was telling her that I had been on tinder to try and start drama. I called her around when the show was supposed to end and she wouldn't believe me and proceeded to sleep with him. They never even went to the show because she forgot her ID. She's apologized but still doesn't trust me.
Do I break up with her?
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