How to manage an angry customer who has all the right to be mad, while your company is totally wrong?

It is necessary to listen carefully to him without interrumpt him then apologize politely and try to correct the mistake, provide him with a special service and favorate him

The best way is to listen to the customer and never interrupt them while they are expressing their complain.  Apologize and give the assurance that this will be taken seriously.  If to the extent that the customer require or requests for the higher manager's presence then give him the opportunity but make sure that you will pass the full story to the manager to avoid letting the customer repeat themselves because this will make them more upset (like opening the wound again and again).

Emphatized. Make sure that you acknowledge their problem first. Make them feel that you are on their side, without putting your company in a bad light. Highlight that you will help them because the company doesn't tolerate bad practices. Provide the best solution to their problem immediately, and during all these, if the customer is still ranting, let them. Put in mind that the customer isn't attacking you personally. They are just venting out their situation. Go extra mile in extending help, provide credits/vouchers (only if the company allows it) this would guarantee repeat customer once accepted. Tell them you will document everything and will file a report. It will make them feel valued. Lastly, once you solve the situation, ask if they still have concerns. End the conversation with a thank you and a smile.

When I am dealing with such customer, I keep one thing in mind that I am the face for the company for that customer and he has every right to feel the way he is if he is mistreated or mislead , so would allow him/her to vent out completely and then reason him with apology and empathy and will address his/her issue immediately by providing correct resolution.

I would deal with them first by saying an apology on behalf of the company. Then I would talk to them wholeheartedly about their complaint/s. I would listen to everything they have to say and after that I would explain the company's side. Most importantly I would talk to angry customers with a low but still dignified tone. Because we should always remember that is them who keep our company running.

LISTEN CAREFULLY TO HIM AND HIS QUERIES, DO NOT INTERUPT HE/SHE IN BETWEEN. MAKE HIM FEEL THAT HIS/HER QUERIES WILL ENTERTAINED WITH A SATISFACTORY ACTION

There was a similar question recently - please see my long answer here