The quadratic trigonometric equationacos^{2 }x+bcosx- 1 = 0 has the solutions (π/3), (π), and (5π/3) in the interval 0 < x < 2π. What are the values ofaandb?

I don't even know where to necessarily start with this question. Should I sub a certain value in for x? I tried that without any success.

The answers are a = 2 and b = 1. Any suggestions would be very helpful, thanks in advance!