What is the probability an Eisenstein integer is visible from the origin (that is, a line from the origin to the integer does not intersect any other Eisenstein integers)?

Note: An Eisenstein integer is a complex number of the form \(a+b\omega\) where \(\displaystyle \omega = \frac{-1+i\sqrt{3}}{2}\) and \(a,b \in \mathbb{Z}\). For example, \(1, \omega\) and \(3+2\omega\) are all Eisenstein integers.

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