1996 AIME Problem 11

Let P be the product of those roots of z^{6}+z^{4}+z^{3}+z^{2}+1=0 that have positive imaginary part, and suppose that P=r\left(\cos \theta^{\circ}+i \sin \theta^{\circ}\right), where 0<r and 0 \leq \theta<360. Find \theta.