I'm not a huge fan of the "I understand, you feel angry, etc. " method of validation unless it's really something I understand from personal experience. Same goes for "I'm sorry you feel . . ." - it's too easily confused for an apology.
I prefer to say things like "You sound angry.  :)id something happen?" It's less triggering.
Also, you don't always have to validate. If it isn't working, you can simply end the conversation or move on.