The greatest literary work of ancient Tamil literature during the Sangam age is considered to be the Ettutogai (Eight Anthologies). Here's why:

Overview:
The Sangam Age is a period of ancient Tamil literature that lasted from 300 BCE to 300 CE. The Sangam literature was composed by poets and bards who were part of the Tamil Sangam, a gathering of Tamil scholars and poets. The Sangam literature is divided into two categories: the Ettutogai (Eight Anthologies) and the Pattupattu (Ten Idylls).

Significance of Ettutogai:
The Ettutogai is a collection of eight anthologies of poems that were composed by various poets. These eight anthologies are Ainkurunuru, Kuruntokai, Narrinai, Akananuru, Purananuru, Agananuru, Pathupattu, and Paripaatal. The Ettutogai is considered to be the greatest literary work of the Sangam Age as it provides a glimpse into the culture, society, and beliefs of the ancient Tamils.

Content:
The poems in the Ettutogai cover a wide range of topics such as love, war, nature, ethics, and morality. They provide insights into the lives of the people during the Sangam Age, their customs, traditions, and beliefs. The poems also showcase the diversity of the Tamil language and the poetic styles of the various poets.

Influence:
The Ettutogai has had a significant influence on Tamil literature and culture. The poems have been studied, analyzed, and celebrated for centuries, and have inspired countless poets and writers. The Ettutogai has also played a crucial role in the development of the Tamil language and its literature.

Conclusion:
In conclusion, the Ettutogai is considered to be the greatest literary work of the Sangam Age as it provides a unique insight into the ancient Tamil culture and society. The poems in the Ettutogai are a testament to the rich literary tradition of the Tamils and continue to inspire and influence Tamil literature and culture to this day.