How Is Trigonometry Related To Polynomials?

Algebra Level 5

f(x)=x8x6+x4x2+1 f(x)=x^8-x^6+x^4-x^2+1

Let a=p+qia=p+qi be a root of the above polynomial where the imaginary part qq is maximal (over all roots). Write q=sin(t)q=\sin(t) for a positive acute angle tt, measured in degrees.

Enter the minimum value of tt as your answer.

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