Great Radical Equation

Geometry Level 3

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

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