S1·E52 Radical Dreamers

During Golden Week, Hayate, Nagi, and Maria take a trip to an island in the Aegean Sea. Nagi still does not like to go outside much, though she gives in to Hayate after he sulks. While out the next day, Nagi's hat is blown away by the wind, and when Hayate goes to retrieve it, he falls into a time slip and arrives many years previous when Nagi was living on the island. After he realizes what is going on, he discovers she is being targeted by the Mafia, and he ends up protecting her from them, ultimately winning; Hayate realizes that the reason he was sent back was to save Nagi. Hayate had promised Nagi in the past to watch the stars together at the beach, but when they go at sunset, Nagi's hat once again is blown away and Hayate goes through another time slip back to the present. This caused Nagi to remember Hayate in the past as a liar who disappeared on her and took her hat with him. Back in the present, Hayate gives Nagi back her hat and the two gaze at the starry night sky together.