All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Muslims celebrate only two feasts and there is no third feast in Islam. The two feasts are ‘Eed Al-Fitr and ‘Eed Al-Adhha. Anas reported that the Prophet came to Madeenah and found them that had two days in which they played. The Prophet asked: “What are these two days?” They replied: “These are two days we used to play in, in the Pre-Islamic Era of ignorance. Thereupon, the Prophet said: ''Allah replaced them with two better days: ‘Eed Al-Fitr and ‘Eed Al-Adhha. ‘Eed Al-Fitr is celebrated on the first day of Shawwal when the month of Ramadan ends, whereas, ‘Eed Al-Adhha is celebrated on the tenth of Thul-Hijjah; this day is also called the day of Sacrifice.
Before this day, i.e. the ninth of Thul-Hijjah, all the Muslims who perform Hajj gather at mount Arafat, and gathering there is one of the pillars of Hajj.
Hence, if the questioner is inquiring about the date of the coming ‘Eed according to the Gregorian date, then we bring to his attention that Islamic ‘Eeds depend on the sighting of the new moon. So, it can only be decided after sighting the moon of Shawwal and the moon of Thul-Hijjah. This is the most correct opinion of the scholars.
Allah knows best.