Does the third divorce take place with the utterance "You are divorced, and this is the third" with the intention of ending all divorces, knowing that the wife is in a state of purity and intercourse has occurred, and is living with her considered forbidden?

Your wife has become irrevocably divorced (baynunah kubra), and you cannot take her back unless she marries someone else – a marriage of sincere intention, not for the purpose of making her lawful for you (tahlil) – and the new husband consummates the marriage with her, then divorces her or dies, and her waiting period (iddah (definition)) from him ends. The validity of the divorce is not negated by your anger, as long as you have not lost your sanity, nor by the fact that the wife was in a period of purity (tuhr) during which intercourse occurred, nor by the two final pronouncements of divorce occurring consecutively without a return (raj'ah) or a new marriage contract. This is the view of most scholars.