Is this necessary to control your facial expression while having dialogues with an angry customer who is not ready to convince with you?

Yes, to handle an angry customer is a challenge. It is very important to console, make him cool down and politely listen to manage the customer grievances and complaints. Self control and self discipline are the keys for excellent customer service.

Yes, this very important to control your facial expression, that play an important role in convening the customer special eye contact and smile on face. Most of the time the customer scrutinize the facial expression and resulting in lack of rudeness and resentment. 

It is best to control your facial expression because it times, the facial maybe in a negative or judgemental to the customer which may hinder the cuatomer to say out his views because he may feel being judged.