I caught my long distance boyfriend cheating on me, should I break up with him?

I'm in a long distance relationship, we met three months ago, he tells me that he loves me & I am the first thought on his mind when he wakes up and wants a future with me. We Skype video call 6+ hours a day, my family knows about him and his mother and father know about me I've met his parents on Skype.

This random girl found my Skype a screen shot of my boyfriend being flirty and sexting her.

I was upset and hurt me, I forgave him.
I couldn't believe anything he told me anymore, two months later I needed to find out if he was still being unfaithful so I made a fake account on social media and sent him a message along with photos of a decent looking girl who had semi nudes, he caught the bait after I kept sending him messaging until he finally replied, they started talking and he asked where I lived and I told him that I lived close to his city, I asked him if he wanted to hangout and he agreed and told the profile that she looked sexy, etc.

when I would stop responding to his text he would text the profile.

He has no idea that I was the one behind the profile & he believes that I was one of my friends because I told him that my friend sent me screen shots.

He cried and told me he didn't cheat & definitely wouldn't ever if we were together in real life.

I feel that since this happened I don't really trust him anymore, I am not stressing about it anymore because I know the truth.

He addmited to me that he can't really trust because of his past relationships the girls were unfaithful, I am faithful but he says he can't %100 trust me because I have a lot of guys in social media who message me.

What should I do? Do you think he is cheating out of bordom, when he isn't talking to me? Insecure? Do you think flirting and sexting is cheating? Do you think I should dump him and wait until we actually meet in person to decide our relationship?
He says that he doesn't want to lose me as his girlfriend.

I caught my long distance boyfriend cheating on me, should I break up with him?
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