Does a divorce take place if the husband says to his wife, "Go, you are divorced," in a state of extreme anger, intending to threaten rather than to effect a divorce? And how should the wife respond if it does take place, knowing that this is the first time?

If a husband says to his wife, "You are divorced," the divorce takes effect, and it does not depend on intention, even if he meant it as a threat. Anger does not prevent the divorce from taking effect as long as the husband understands what he is saying. The husband can take his wife back by saying: "I take you back" or "I have taken you back," and it is recommended to have witnesses for the reconciliation. Respect and understanding should prevail between spouses, and the treatment for 'nushuz' (marital discord/rebellion) is explained in the Qur'an. Anger is from the gates of Satan, and one must be careful not to stir up problems in front of children due to the negative impact it has on them.