\(15\) 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.
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.