Luke 1:26 - 35 Mary is visited by an angel in the 6th month of the year, telling her she will concieve...?

It's already been argued that the shepherds were watching their flocks by night because the ewes were lambing and the shepherds had to be on hand in case of a problem birth, which would put Jesus' birth in the springtime. Easter, however, has nothing to do with the birth of Jesus; the date is determined by calculated from the Jewish Passover, which was the subject of celebration at the Last Supper. But considering the two dates are so close to coinciding, I have this nagging suspicion that Jesus actually died on his birthday. That would be incredibly sad....