2018 circles

Geometry Level 1

The two rays in the diagram make an angle of 60.60^\circ. The first circle is tangent to both rays and has radius 1. Each successive circle is tangent to the two rays and externally tangent to the previous circle.

The radius of the 2018th is aba^b, where aa and bb are positive integers with bb maximized.

What is a+ba+b?

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