<human>: Can you condense the text into three sentences or less?

So to be brief, back in May my boyfriend admitted he liked a new friend of his.  We live together, and he was very obviously sneaking out at night and staying out all night.  One time I caught him getting in her car.  He denied anything but friendship, but one night he was texting like crazy, and I saw a few of them, he was calling the girl out about "using him".  I confronted him, he broke down and cried and admitted to cheating.  It was a rough emotional time, and we nearly broke it off and moved out, but we got through it, and everything was good... so I thought.

Anyway, last night he left his gmail open on my computer, and I couldn't help but check, and sure enough he's sending her e-mails saying "Glad I got to see you again last night, you're so beautiful, I can come over again next week."  Granted this isn't proof of fornication, but it's proof of an emotional affair where there once was fornication, and if he's sneaking off to her place and calling her beautiful and meanwhile telling me he hates her guts and doesn't respond to her texts, I know what's going on.

I still have his e-mail open, and I'm trying to think of anything I can do to route the two of them into a confrontation.  I know what has to be done, I have to tell him I saw the e-mails, the he broke my trust and that we can't be together anymore and that he has to move out.  This girl has been especially evasive with me and I have always offered to peacefully talk about it, but when I've confronted her in person she lies to my face and then texts him insulting garbage about me, so yes I have somewhat of a vendetta and would at least like to get some vindication.
<bot>: Boyfriend left g-mail open on my computer, found confirmation of cheating, looking for good way to use this e-mail access situation to my advantage for non-violent confrontation and vindication.