Faced with aggression or distress, I get very calm and focus intently on the person, project a "let's work this out together" attitude, and gradually bring them to a calmer, more reasonable state. Basically, Jedi mind tricks It's never failed me, either with authorities or assailants, in my adult life.

While I won't vouch for the point-by-point accuracy, Scientology's Tone Scale sums up this approach pretty well:
Spoiler for big pic:

The idea is that if you're faced with hostility, you can't respond with enthusiasm--you might as well be speaking another language. You need to bring your tone down to within a couple levels of the other person in order to connect, and then you can gradually bring them up.