How Is Trigonometry Related To Polynomials?

Algebra Level 5

\[ f(x)=x^8-x^6+x^4-x^2+1\]

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

Enter the minimum value of \(t\) as your answer.

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