Some terrific answers and questions here. I was taught that trying to deal with an "angry, upset or rude" customer or prospect was futile until you find out what the root cause of the condition is.
I learned years ago to simply say "I can't help noticing you seem (upset, angry,etc). Sounds to me as if somewhere along the way you've had a bad experience. Would you mind telling me what it was so I don't make the same mistake?"
First, they get to vent which will usually take all the steam out of them. If you pay attention during their discourse they will also tell you exactly what NOT TO DO in order to make them a customer?
Does it work every time? No. Nothing works 100% of the time in sales. All any of us can do is increase our probabilities for success at every opportunity.