Hello the equation I want to solve for 0 <= x <= pi

$\displaystyle 3 cos^2 x + 2 sin x - 3 = 0$

This is what I have so far:

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

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

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

sin x (2 - 3sin x) = 0

roots: x = 0 or 2/3

Is this correct? But now what? Do I calculate cos(0)? and cos(2/3)?

Angus