February 29th.
Applying this value to n I get a declination of 8.29 ° value very close to 8.183 °.
At n equal to 284 is October 11
Applying this value to n I get a declination of 8.10 ° also it very close to 8.183 °
Reflecting on the dates it gets is much more impressive but also more realistic to think that the date is that of February 29 because it is the day that is inserted into the leap year and is the only day that exists once every 4 years, doing the Exceptions (see Gregorian Calendar).
Even the resemblance between our Gregorian and Egyptian calendar makes it much more likely that this day of the year is right.