what are the zeroes of the graph 2sin(squared)x + cosx-3 = 0

Write it as a polynomial in cosx and solve for cosx.

2(1 - cos^2x) + cosx = 0

2 cos^2x -cosx -2 = 0
That can be factored to give

(2cosx +1)(cosx -1) - 0

cosx = -1/2 or +1