1984 AIME Problem 8

The equation z^6+z^3+1=0 has complex roots with argument \theta between 90^\circ and 180^\circ in the complex plane. Determine the degree measure of \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.