How does one analyze and reconcile with a wife divorced by three pronouncements during a period of anger, based on a fatwa that considers it a single pronouncement?

Anger does not prevent the occurrence of divorce unless it removes one's sanity. If you divorced your wife with three pronouncements of divorce, and then you were issued a fatwa that only one pronouncement occurred, and you acted upon the saying of trustworthy scholars, then you may reconcile with your wife before her waiting period ends by saying: "I have taken you back," and it is more cautious to have witnesses, or by engaging in sexual intercourse according to some scholars. However, if three pronouncements of divorce are completed, then your wife has become irrevocably divorced from you (baynunah kubra), and she is not lawful for you unless she marries another husband out of genuine desire, and he consummates the marriage with her, and then he divorces her or dies, and her waiting period from him ends. As for a tahleel marriage (a marriage solely to make her lawful for her first husband), it is forbidden and void and does not make her lawful for her first husband.