When the moon sets actually varies depending on the moon's phase. The new moon rises and sets more or less when the sun does, first quarter rises mid-day and sets mid-night, etc. I've also heard of that being a magically charged time, though. I've also heard that 3 AM may be of magical importance because it is often the darkest time of night, but I honestly do not know if this is true.
In this case you may be waking up for supernatural reasons, or you might just be reverting to an older human sleep pattern; http://www.nytimes.com/2006/02/19/opinion/19ekirch.html?_r=3
Until fairly recently in human development we naturally slept in two segments each night with a period of waking in between. People will sometimes revert to this sleep cycle and think something is amiss because we have this notion that one should remain unconscious the entire night. It can be inconvenient for those with work or school in the morning, but it's nothing unhealthy or out of the ordinary. Just find something low-energy to do for a while like read or listen to music and you should feel tired again in around an hour.