Source of classic drama: detective with regret upset over some days in Rome (9)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

PI (abbreviation for private investigator = detective) + RUE (regret), all reversed (upset = upwards in a down clue), then IDES (in the Roman calendar , either the 13th or 15th day of each month, therefore “some days” of the year). Ancient Greek playwright .