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.