Trig-gono-metry-2

Geometry Level 3

The perimeter of the octagon formed by the roots of the polynomial equation \(z^8-256=0\), plotted in the complex plane in the order can be expressed as \(a\sqrt{b-\sqrt b}\), where \(a\) and \(b\) are positive integers with \(b\) being square-free. Find \(a+b\).

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