What is the ruling of Islamic law regarding a man divorcing his wife twice in a state of extreme anger, knowing that there was a prior agreement to divorce if the wife committed a certain act, and she did commit it?

Your promise to divorce does not entail anything. However, your subsequent divorce does take effect. Your anger at the time of uttering the divorce does not prevent its validity, as long as you uttered it consciously and were not overcome in your intellect. The two divorces have taken effect as long as you uttered the divorce twice, unless you uttered the divorce the second time with the intention of affirmation and informing of the occurrence of the first divorce, in which case the second divorce does not take effect. If you have not divorced her thrice, you may take her back during her waiting period (iddah).