EID OR EED
A `Eed is any day of gathering. It is derived from `Aada (meaning returned), because people return to it periodically. Some scholars say that it derives from `Aadah (custom or practice) because people are accustomed to celebrating it. Its plural is A`yaad. Ibn ul-`Araabee said: "It is called `Eed because it returns every year with renewed happiness.” Lisaan ul-`Arab
Ibn Abidayn said: “The Eid days are thus named because Allah renews His Bounties in them; and He distributes His blessings to His worshipers. From these are Fitr (eating), after food had been prohibited and Sadaqaat al-Fitr (the charity of breaking the fast) to the needy. And on Eid al-Adha, the completion of Hajj with the final Tawaaf of visiting; the meat from sacrifices and many other acts. Also because the custom in Eid is joy, happiness, cheerfulness and gladness.” [Hashiyah Ibn Abidayn (2/165)]
Islamically, Eid is a day on which Allah (Glory be to Him) showers His servants with His blessings and generosity. So at this time that the merciful Allah (Glory be to Him) extended his generosity, how great it would be for pious people and sinners to confess (their defects and faults), and hope for receiving His grants.
From authentic hadeeths that are cited above and subsequently, it is concluded that the Muslims have only three `Eed days, a weekly `Eed every Friday, and two annual `Eeds: al-Fitr and al-Adha.
It becomes clear then that:
Anas (R) said: “The Prophet Muhammad (May Allah honor Him and grant Him peace) came to Madeenah and the people of Madeenah had in Jahiliyah two days of play and amusement (they are the day of Niarooz (New Years Day) and the day of Maharajaan (Final Day of the Year). So, The Prophet Muhammad (May Allah honor Him and grant Him peace) said: "I came to you and you had in Jahiliyah two days of play and amusement. Indeed, Allah has replaced them for you by that which is better than them: The day of Nahr (slaughtering) and the day of Fitr (breaking fast)." Musnad Ahmad Vol 3: 103, 178 and 235. 
By Allaah's blessing and mercy, Islaam contains the complete and perfect guidance for humanity. Allaah (SWT) said: This day I have perfected your religion for you, have completed My favor upon you, and have chosen for you Islaam as your religion. Quran 5:3
Islaam did not neglect any information needed by people to achieve happiness and avoid harm, in all matters - small or large. It informs them of all that would save them from the Fire and let them into the Gardens in the Hereafter. This was the mission of all of the prophets, as declared by Muhammad (S), Never was a prophet before me, but he disclosed to his people what he knew to be best for them, and warned them of what he knew to be evil for them. Sahih Muslim
a) Islaam contains the complete and perfect guidance for humanity.