It is quite likely that the break-up process started when the stern was at an angle of 11 to 12 degrees to the sea level. In his book RITLOT-SST: A Centennial Appraisal, Sam Halpern demonstrates convincingly that the bending stress on the Titanic keel reached its maximum at 11 to 12 degrees; theoretically, if the break had not started then, it might not have happened at all because as the stern rose higher, the bending stress on the keel dropped sharply.
We must consider what we mean by "start" of the break-up. It is quite likey that when the stern reached around 11-degrees, the keel structure started to give way probably at its top surface between the 2nd and 3rd funnels. But IMO it was not an immediate "snap!" and so for a short time the failing keel still supported the hull and so the stern continued to rise. It was at that time that the dipping bow caused the Titanic to suddenly lose its longitudinal stability (a separate event) resulting in that sharp downward plunge that generated the well known "wave". When that happened, the stern rose further even though the keel was breaking (and that rise would have momentarily reduced the bending force) and probably reached an angle of around 25-degrees before the failing keel snapped and the full break-up, as witnessed by many survivors, occurred.
If makes you wonder if that’s what the first “explosion” was. Survivors mentioned some rumbling or an “explosion” as the bridge dipped under. Maybe that was the keel popping upward. And then the second “explosion” is the louder one accompanied with the stern settling back.