To simplify this equation, we can use the Pythagorean identity: sin^2 x + cos^2 x = 1

Therefore, sin^2 x = 1 - cos^2 x

Substitute sin^2 x = 1 - cos^2 x into the equation:

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

Expanding the equation:

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

Rearranging the terms:

This is a quadratic equation in terms of cos x. To solve for cos x, we can use the quadratic formula:

cos x = [-(-1) ± sqrt((-1)^2 - 4(-3)(6))]/(2(-3))

cos x = [1 ± sqrt(1 + 72)]/(-6)

cos x = [1 ± sqrt(73)]/(-6)

Therefore, the solutions for cos x are:

cos x = (1 + sqrt(73))/(-6) or cos x = (1 - sqrt(73))/(-6)

Since sin x = sqrt(1 - cos^2 x), we can find the corresponding sin x values using these solutions for cos x.