Given that the radius of larger circle is \(R =2\), find the radius of smaller circle, i.e. \(r=?\)

**Details and assumptions**:-

- The smaller circle is tangent to :-

\(1)\) The arc which subtends an angle of \(60^\circ\) in the opposite arc.

\(2)\) The two radii that join endpoints of the arc to the center of the circle.

- Round your answer to 2 decimal places.

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