360TripleView: 360-Degree Video View Management System Driven by Convergence Value of Viewing Preferences

360-degree video has become increasingly popular in content consumption. However, finding the viewing direction for important content within each frame poses a significant challenge. Existing approaches rely on either viewer input or algorithmic determination to select the viewing direction, but neither mode consistently outperforms the other in terms of content-importance. In this paper, we propose 360TripleView, the first view management system for 360-degree video that automatically infers and utilizes the better view mode for each frame, ultimately providing viewers with higher content-importance views. Through extensive experiments and a user study, we demonstrate that 360TripleView achieves over 90\% accuracy in inferring the better mode and significantly enhances content-importance compared to existing methods.