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The end of Acts leaves us with Paul under house arrest, waiting to see Caesar, but he was later brought before Nero, who died in the year 68 AD, see Wikipedia. It is generally reckoned that Paul was executed by Nero, so Paul, also, would have departed this life on or before that same year.
So it would seem unlikely, or even impossible, that the incident in Acts 21:18 refers to 69 AD.