In the CARP system, we recognize that an angry person is not "ready" to work with you to solve a problem. Likewise for someone overcome by any other emotion. Think about a situation, let's say with a spouse, where you were so angry that you had no interest in being constructive, at least at that point. It's the same. We often forget that our customers share this quality of losing the ability to do constructive problem solving when angry, even when it's to their benefit to do so.
Dealing With The Customer's Feelings First
It's a basic and essential tenet to get your timing right. The first task, beyond staying in control of yourself, is to de-escalate the intensity of emotion on the part of the customer. If you move too quickly to get and give information with the customer, the person is likely to get angrier. You have to acknowledge the feelings first, and create rapport, before the good, constructive stuff can happen.