Trigonometry+Polynomials=Trigonomials

Geometry Level 5

8x36x+1=0\large 8x^3-6x+1 = 0

If aa, bb and cc are the roots of the equation above, find the value of cos1a+cos1b+cos1c\cos^{-1} a + \cos^{-1} b + \cos^{-1} c in degrees.

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

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