Does a divorce take place in the aforementioned situation, which occurred during intense anger, and what is the procedure for reconciliation if it does?

If the husband's anger reaches the point of delirium, where he loses awareness and intent of what he says and does, then his divorce does not take effect. This is because he is considered in the same category as one who is insane or coerced, and the hadith "No divorce in ighlaq" applies to him. However, if he is aware of what he is saying and intends it while angry, then his divorce takes effect.