AIME problem

Geometry Level 5

A regular \({12}-gon\) is inscribed in a circle of radius \({12}\). The sum of the lengths of all sides and diagonals of the \({12}-gon\) can be written in the form \(a + b \sqrt{2} + c \sqrt{3} + d \sqrt{6},\) where \(a^{}_{}\), \(b^{}_{}\), \(c^{}_{}\), and \(d^{}_{}\) are positive integers. Find \(a + b + c + d^{}_{}\)

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