And they stood and betrayed (ἐξηγόρευσαν) their sins and the iniquities of their fathers. And they stood at their places and they read in the scrolls of the Law of the Lord their God and they were announcing (ἐξαγορεύσοντες) to the Lord and worshiping the Lord their God (2 Esdras 19:2-3).The key term here comes from the ἀγορά, the Greek market place, where people bought and sold their wares, and there people came to hear the latest thought and news. So the verb to buy was ἀγοράζω and to speak in public was ἀγοράομαι which became in Koine Greek ἀγορεύω.To publish news or announce something in public was ἐξαγορεύω. To publicly announce a secret or conspiracy was to betray it, so ἐξαγορεύω could also mean to betray.
The Hebrew term used here (Nehemiah 9:2) is yitwaddu (mitwaddim in verse 3) which is usually translated confess and is part of repentance under the Law of Moses (Leviticus 5:5). So according to Esdras sins are not just to be admitted, they are to be betrayed.