Well, there is no technique on Earth to get the boss to admit that he has made a mistake or make him repent or improve on his behavior by a subordinate. Believe me, you may read thousands of topics on "How To Deal with a Boss" online, in books, or articles, but a bad boss always remains a bad boss.
Now coming to your point, are you interested in knowing how to digest insults by your boss? Or are you wanting to know how to react to the situation?
If you want to know how to digest insults, start learning to be shameless like so many bosses do in front of their top boss. That's the way you get paid for hearing insults and humiliation and continue a long career in a company. Put a smile every time you are insulted, and if your smiling provokes more insults from your boss, learn to say SORRY for no reason at all. Learn to be Deaf, Dumb, Blind, and better still Brain Dead. Practice makes a Man Perfect.
If you want to know how to react to the situation, then here it goes: First, find out what makes your boss angry. Is it something related to your work performance or attitude? Are you responsible for making him behave in such a way? Are you good at the job that you do? Are you being made a scapegoat for someone else's mistakes? Can you rectify yourself and improve on the same? If you come out clean from most of the introspection, then you should now ask your boss what is the reason for him hurling abuses at you, and that too in front of other employees. You get paid for doing the work assigned and not for hearing abuses. Report it to the top management with a grievance letter stating the same, maybe to HR and any other higher-ups. If the higher-ups are in favor of your boss and you are sure nothing is going to come out of it and they might retaliate, then in that case, START LOOKING OUT FOR A BETTER JOB. A day's life with dignity is much more than a lifetime of disgrace. Regards