Hi there, Rob IELTS here. "I believe that..." is simply stating the persons belief. "I happen to believe that..." sounds like the speaker thinks they are making some sort of moral stand, perhaps in (contrasting) response to another speaker having said something they disagree with. It kind of adds a bit of emphasis to their belief. e.g. A: Would you like a cigarette? B: I happen to believe that smoking is a disgusting habit (speaker B doesn't approve of speaker A's offer) Hope this helps!

Thank you so much for your comments!!! Is it one of those cases where the purpose of changing a little bit the expressions is to emphasize what the speaker want to say?? :)