I used to work in customer service and I think you have to adapt the approach a little bit depending on what type of customer you have. You can't have a one phrase fits all. An angry old lady needs to be dealt with in a more sympathetic manner and probably for a longer time, than an irate business man whom is short of time and just wants to hear that you really will sort it out.

A good opening is "I am sorry to hear that you are having problems, I want to help sort it out."

One trick I learned was if they are shouting , to talk more quietly, they have to stop if they want to hear what you propose to do. You need to be able to keep calm, never shout back no matter how loud they are and remember, if you really do help them, they will remember and hopefully the company will not lose their custom.

In my experience, I've found it successful to start off by having the customer tell me the issue. It's no secret that people like to talk about themselves, so when you get the person on the line say, "Sir/Ma'am, I'm here to help you get this handled, would you mind telling me about the issue at hand?" Let them talk, get all the information so you can come up with a workable solution.

Personally, I don't like it when a customer service rep try's to "sympathize" with me or says they "understand" what I'm going through. The best service I've gotten when upset is that the rep let me tell my story, he acknowledged my upset with a quick "thanks for letting me know, now let's get this fixed". He instantly gave me a simple solution right then and there. Boom, done, handled!

Hope this helps!

Best,
Ferris Stith
Social Media Manager
PostcardMania.com

Staying relaxed in spite of being faced with an irate client requires the right attitude and fortitude. One of simple way to handle an angry client as a customer service representative is to master the art of empathy by conceptualizing your client's plight, you will have a much clearer perspective of your customer's problem. Thus, one of the proven methods to deal with angry clients is through the art of listening and by being compassionate, as well as discerning of his current state.

Once you have displayed the right attitude in the face of a very violent atmosphere, then I assure you that things will be handled as it should be and you will be able to find resolution whatever your customer is currently experiencing.

Listed below are some of the things you should say to an angry customer, courtesy of Suite101.com:

“Thanks for taking the time to give us your feedback. I’ll pass on those comments to management.”
"Thanks for being so frank and honest with what you have to say about the bad service you have received.."
"I'm sorry you've had such a bad experience. I'd like to try and help."
“I’d be upset too if that happened to me. I know how frustrating it can be."
"What's happened to you is clearly unacceptable. Let me assure you I fully intend to fix the problem."
"Don't apologize for being angry. It's completely understandable."

Source:
http://www.suite101.com/content/what-to-say-to-angry-customers-a305619