Let's rewrite sin^2x as (1-cos^2x) using the Pythagorean identity:

2(1-cos^2x) + 2sin2x + 1 = 0
2 - 2cos^2x + 2sinx cosx + 1 = 0
2cos^2x - 2sinx cosx + 3 = 0

Now, using the double angle identity sin2x = 2sinx cosx, we can rewrite the equation:

2cos^2x - sin2x + 3 = 0

Now, we can substitute sin2x with 2sinx cosx:

2cos^2x - 2sinx cosx + 3 = 0

This equation cannot be simplified further without additional information or techniques.