What is the ruling on cohabiting with one's wife after two previous divorces, followed by a third divorce that occurred in a state of extreme anger, knowing that the muftis have differed regarding the validity of this third divorce?

Divorce pronounced in a state of anger is effective according to the consensus of the Imams, unless the anger reaches a level where the person loses perception and awareness of what he is saying. This is what is meant by the "Ighlaq" (closure/compulsion) mentioned in the Hadith. A Muslim should avoid the causes of anger.