Great Radical Equation

Geometry Level 3

4x1x22=0 4x\sqrt{1-x^2} -\sqrt2 = 0

For x[1,1]x \in [-1,1], the roots of the equation above can be expressed in the form cos(1nπ) \cos\left( \frac 1 n \pi\right) and sin(1nπ) \sin\left( \frac 1 n \pi\right) , where nn is a positive integer.

Find the value of nn.

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