How can i ask him to forgive me?

Alright so i have been dating this guy for almost 2 years. We just had a major fight last night and i was really angry saying things like nothing between us matters, and that i don't care for him, and such. He got really angry and broke it off, followed by hanging up on me. I called him back and sat there explaining how much he matters to me and that i need him in my life. After 2 hours, he finally decided to take me back. I told him how sorry i was about that and that my best friend set me off and that he was the one i took my anger out on. We talked about how i shouldn't have taken it out on him and he shouldn't have reacted like that. We then decided to go to bed, by now it was 3am. So we both woke up some time after noon. We started talking on the phone some and got talking about how he didn't fully forgive me for this. This isn't the first time this has happened. He brought up that i said last time it wouldn't happen again. I told him this time i would give him my word and mean it wouldn't happen again if he could forgive me. He then went on to tell me that i need to prove it to him that it would not happen again. I asked him to tell me how to prove it and he responded with that is what i need to figure out. I am asking for advice on how to prove to him i will not cause anymore problems like this again.