\(15\) billiard balls are lying on a table in such a way that they are just crammed inside an equilateral triangular frame in a neat and perfect manner. Given that the frame's perimeter is \(876mm\), determine the radius of a single billiard ball.

**Details**:

Record your answer in

**millimetres**.Answer can be given up to

**\(3\) decimal places**.You may use a calculator to evaluate the final expression of the answer.

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