ויאמר המלך לחכמים ידעי העתים
“And the King said to the wise men who knew the times.” (Esther 1:13)
The Gemara in Megillah (12b) explains that, “the wise men who knew the times” were the rabbis who knew how to calculate leap years or determine the day of Rosh Chodesh. Why would Achashveirosh seek their council about what to do with Vashti?
R’ Yonason Eibshitz (Yaares Devash, Vol. 1, Derush 17) explains: The Gemara in Rosh Hashanah (3a) says that the years of the non-Jewish kings are counted from Tishrei; i.e. if one became a King a few months before Tishrei, when Tishrei arrives he starts the second year of his rulership. The party, which was “in the third year of his reign” (1:3), started in Tishrei. The Medrash observes that in the phrase: ימים רבים שמונים ומאת יום - “many days, one hundred and eighty days” (1:4) — the words, ימים רבים, are apparently superfluous. The Medrash explains that since the minimum of a plural is two, ימים means two days and רבים refers to another three days. This teaches us that before Achashveirosh started the one hundred and eighty days of festivity, he held a private party which lasted five days. Thus, the one-hundred-and-eighty-day feast commenced on the sixth of Tishrei.
Counting from the sixth of Tishrei and calculating based on alternative months of twenty-nine days and thirty days, one hundred and eighty days later would be on the eighth of Nissan. Consequently, the last day of the seven-day festive meal for the people of Shushan, at which he called for Vashti, was on the fifteenth day of Nissan.
Vashti was the daughter of King Balshatzar, who erroneously calculated that Hashem would no longer take the Jews out of exile and that he was thus the sole owner of the vessels of the Beis HaMikdosh. He celebrated this on the night of Pesach — the fifteenth of Nissan — and by heavenly intervention he was killed instantly (see Doniel 5:30, Haggadah Shel Pesach, Vayehi Bachatzi Halailah). Therefore, this day marked the anniversary of her father’s passing and was an occasion for great mourning.
Achashveirosh loved Vashti and endeavored to minimize the iniquity she had committed against him. Consequently, in retrospect he thought that since she had been in mourning for her father’s death that day, it had been wrong of him to call her to make a grand appearance before the people on that day and she deserved to be dealt with compassionately.
However, if the third year of Achashveirosh’s reign was a leap year, then the festivities actually culminated on the fifteenth of Adar Sheini and Vashti had no justification for her disobedience. Consequently, he called the rabbis who were experts on setting the Jewish calendar, hoping that they would tell him that it was not a leap year, thus providing him with a way to save his beloved Queen Vashti.