Trigonometry+Polynomials=Trigonomials

Geometry Level 5

\[\large 8x^3-6x+1 = 0\]

If \(a\), \(b\) and \(c\) are the roots of the equation above, find the value of \(\cos^{-1} a + \cos^{-1} b + \cos^{-1} c\) in degrees.

If you think that roots exist outside \([-1, 1]\), write 272 as your answer.

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