Lies and cheating

I've been with my boyfriend for 4 years now and he's physically and emotionally has cheated on me several times through the years. I've recently hacked into some of his accounts and found out he messaged his ex last week. He denied it, even though I had the proof. I asked the ex and she just went on there and blocked him. I then found in his email he's been messaging a woman for the past 4yrs all kind of sexual messages. Nothing new since last year. I asked if he knew her and he said no, I asked if he knew her number and he said no. I saw the emails with my own eyes and he still denies it. I checked the phone logs and he they texted last year. How can I learn to trust him if he can't be honest about everything?