Agnostic atheism is defined as not knowing for sure if any gods exist or not but also not believing in any gods. This definition makes it clear that agnosticism and atheism are not mutually exclusive. Knowledge and belief are related but separate issues: not knowing if something is true or not doesn't exclude believing or disbelieving it.
Agnostic atheism can often be treated as synonymous with weak atheism.
Whereas weak atheism emphasizes the lack of belief in gods, agnostic atheism emphasizes that one does not make any knowledge claims — and usually, the lack of knowledge is an important part of the foundation for the lack of belief. Agnostic atheism is arguably the position held by most atheists in the West today.
Examples:
The agnostic atheist maintains that any supernatural realm is inherently unknowable by the human mind, but this agnostic suspends his judgment one step further back. For the agnostic atheist, not only is the nature of any supernatural being unknowable, but the existence of any supernatural being is unknowable as well.
We cannot have knowledge of the unknowable; therefore, concludes this agnostic, we cannot have knowledge of god’s existence. Bvariety of agnostic does not subscribe to theistic belief, he qualifies as a kind of atheist.
- George H. Smith, Atheism: the Case Against God