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My Boyfriend thinks I cheated?!

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So my boyfriend of a year and a half thinks I cheated on him. The thing is I really didn't. He was cheated on before in the past and had trust issues with women(he admitted that and said that he loves me but doesn't trust me). Situations have come up between us in the past whereby he'd get upset if he saw me talking to a coworker or even my neighbour (both guys) but I'd say hey we were just talking nothing more and I'm not trying to lead them on in any way. We didn't see each other for a whole week (due to work) but we spoke for hours on the phone every night. After that week he saw me talking to another guy at work while i was waiting on him to pick me up and we were laughing and giggling over some nonsense ( but I'm thinking its my coworker why should I be rude) and once again he accused me on leading the guy on and how come we're acting so cool with each other and he believes I'm not the person I make my self out to be and that I have to be seeing another guy. So now he is refusing to answer my calls or reply to my texts. Its been more than 4 weeks now!!!!! I wish he just believe me and stop being so insecure

What should I do?????????????????