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Cognato
He is brother your brother in law.
If your brother-in-law is the brother of your spouse, he is not related to your brother.
If your brother-in-law is the husband of your sister, then he is also your brother's brother-in-law
Your brother-in-law is either the husband of your sister or the brother of your husband. Your brother-in-law is not your husband's brother-in-law.
If your brother-in-law is the brother of your wife, then his brother-in-law is you.
If your brother-in-law is the husband of your sister, then his brother-in-law is you or one of your other brothers.
Either kind of brother-in-law can also have brothers-in-law who are married to other sisters he may have. They are not related to you at all.