We also see in Bereishith, that Havah (חוה) was told by the Snake that on the day she ate from the Eitz Hada'ath her eyes would be opened like the Elohim. (There are places in Tanach where Elohim means Angels)
So it seems to me that Havah ate from the tree to give us the day of Yom Kippur. (One transgression to ensure that your descendants would have a day of divine mercy and forgiveness every year? sounds like a sound investment to me. This happens to also explain the question raised about the Talmud that specifically says אחטא ואשוב twice. Why twice? Once for Havah and once for Adam.)
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