Is the third divorce pronouncement, uttered face-to-face after the wife provoked her husband—who frequently utters divorce when angry and had previously divorced her twice via text messages—in order for him to divorce her, counted, given that he was in a state of extreme anger and hesitation when pronouncing it?

Severe anger does not invalidate a divorce unless it removes one's sanity. An explicit divorce pronounced by the husband after the wife requested it and threatened to leave the house is considered valid as long as the husband was aware of what he was saying and was not coerced. Coercion requires that the coercer be capable, that it is highly probable the threat will be carried out, and that the damage be significant, such as death or severe beating. Spouses must live together honorably and exercise self-restraint, as threatening divorce and frequently swearing by it is a conduct contrary to Islamic law.