When does the muezzin break his fast? Before the adhan, or after it?

The fundamental principle is that a fasting person should break their fast after sunset and the onset of night, based on the Almighty's saying: "Then complete the fast until the night" (2:187). The Sunnah is to hasten breaking the fast after verifying that the sun has set. As for the muezzin, if there are people waiting for his adhan to break their fast, he should promptly make the call, unless he breaks his fast with something minimal that does not delay the adhan, in which case there is no harm. However, if there is no one waiting for his adhan, there is no objection to him breaking his fast before the adhan.