The Days of Tashreeq

The Prophet (saws) said: “The days of tashreeq are the days of eating, drinking and remembering Allah." [Muslim] 

The Prophet (saws) forbade fasting on these days: “Do not fast on these days, for they are the days of eating, drinking and remembering Allah.” [Ahmad, 10286; classed as saheeh by al-Albaani in al-Silsilah al-Saheehah, 3573] 

The days of Tashreeq are the 11th, 12th and 13th days of Dhul Hijjah. SubhanAllah, here is a very interesting connection between eating, drinking and remembering Allah:

Allah says His Book: 
يَا أَيُّهَا الَّذِينَ آمَنُواْ كُلُواْ مِن طَيِّبَاتِ مَا رَزَقْنَاكُمْ وَاشْكُرُواْ لِلّهِ إِن كُنتُمْ إِيَّاهُ تَعْبُدُونَ
O you who believe! Eat the halal/pure food that We have provided you with, and be grateful to Allah, if you truly worship Him alone. [Al-Baqarah:172] 

Notice the connection between eating/drinking and remembering Allah? Eating and drinking, and then thanking Allah is remembrance of Allah. Since Allah used “Oh you who believe” in the ayah, eating then thanking Allah is one of the ways to increase our Emaan. Moreover, it’s an awesome, practical way to show our servitude and gratitude towards Allah for providing for us.
So during these days of Tashreeq (and afterwards), here’s what we should do:

• begin eating and drinking with the Basmallah (Bismillahir Rahmanir Raheem)
• eating with our hands (the 3 fingers of the right hand)
• drinking while sitting down
• saying “Alhamdulillah!” like you mean it afterwards
  

Remembering Allah immediately after the prescribed prayers by reciting Takbeer. This is prescribed until the end of the days of Tashreeq according to the majority of scholars. 
The scholars differed concerning the form of the Takbeer.

1 – The first view is that it is: 
Allahu akbar, Allahu akbar, laa ilaaha ill-Allah, Allahu akbar, Allahu akbar, wa lillaahi’l-hamd (Allah is Most Great, Allah is Most Great, there is no god but Allah, Allah is Most Great, Allah is Most Great, and to Allah be praise).

2 – The second view is that it is: 
Allahu akbar, Allahu akbar, Allahu akbar, laa ilaaha ill-Allah, Allahu akbar, Allahu akbar, Allahu akbar, wa lillaahi’l-hamd (Allah is Most Great, Allah is Most Great, Allah is Most Great, there is no god but Allah, Allah is Most Great, Allah is Most Great, Allah is Most Great, and to Allah be praise).

3 – The third view is that it is:
Allahu akbar, Allahu akbar, Allahu akbar, laa ilaaha ill-Allah, Allahu akbar, Allahu akbar, wa lillaahi’l-hamd (Allah is Most Great, Allah is Most Great, Allah is Most Great, there is no god but Allah, Allah is Most Great, Allah is Most Great, and to Allah be praise).

The matter is broad in scope because there is no text narrated from the Prophet (saws) which specifies a particular form of the Takbeer.