SO sleeping with his EX

Holly
So, last week around wednesday at 1am my SO's phone kept ringing, and he was like "Oh, it's from work". He started his new job in December, and me being nosy saw his call log and turns out he got a call from the same number in November. 
Somehow, i couldn't sleep that night coz it reminded me of his ex who called him at midnight all the way back in Septmeber and he said it a random number was calling him.. When i asked. It turned out to be his ex, he told me that she saw us together and was drunk dialing him. He sent her a msg saying stop calling, they've been broken up for two yrs now and stuff... 
That morning i got a msg from her saying, so u trust this guy? Do u know he has been sleeping with me ever since he got with u? Which is over a year by now?
She send me the screenshot where he begged her not to tell me they were seeing each other. She told me he would run to her everytime we would argue, she knew things about me that i told him bcoz i trusted him.. 
When i got those msgs from her i called him, he declined.. Msgd him that i need an explanation.. He didnt reply.. Then msgd me a few days later, saying so u guys found out have fun. 
This week, yesterday actually he called and was like.. Oh i used to talk to her to get advice on our relationship coz i've known her for so long i am so used to talking to her about everything hut i never fucked her.. 
Honestly, i have qasted a yr of my life.. And he is 29yrs old, how can he act so childish.. We were engaged!!
And this girl, saw our pictures all over his Facebook and Instagram and still met up with him and slept with him? I don't understand people anymore.
Pls, help.. I am so tempted to start an argument with him. But i don't want to seem desperate, coz when he asked to meet up yesterday and the day before i didn't.. Coz I didn't want to fall for his lies anymore.