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 \(0 < r\) and \(0\leq \theta < 360\). Find \(\theta\).

(第十四届AIME1996 第11题)