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In Jewish leap years we add the words
and atonement for transgressions
to a list of things we ask Hashem for in the coming month during the tefilah of musaf on Rosh Chodesh. We do this through the leap month (Adar II) and then we do not include those words the rest of the year, nor do we say them in non-leap years.
Now atonement for our transgressions is a very nice thing to daven for, but what's the connection to leap years or to Adar II such that we only include it when we do?