1996 AIME Problem 11

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.