Way to unlock: Talk to Josephine in Skyhold, relationship is required.
The quest-giver: Josephine (M12,6)
While being in relationship with Josephine (M12,6), talk to her about Antivia. After that, leave her, and after returning when you enter the office a cutscene will trigger. After it "Challenge Josephine's Fiancé to a Duel" operation will be available, and during the conversation you can optionally select the crow icon that it will unlock "Gather Information on Lord Otranto" operation as well.
After completing the operation you will be given an order to go to Val Royeaux. When you arrive there, another cutscene will start. During it you can decide whether you want to start a relationship with Josephine for good, or not.
No rewards for completing this task.