# Problem #285

 285 Let $\mathrm {P}$ be the product of the roots of $z^6+z^4+z^3+z^2+1=0$ that have a positive imaginary part, and suppose that $\mathrm {P}=r(\cos{\theta^{\circ}}+i\sin{\theta^{\circ}})$, where $0 and $0\leq \theta <360$. Find $\theta$. This problem is copyrighted by the American Mathematics Competitions.
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