Stuck on the following - SOLVE:

$\displaystyle 2*sin^2(x) = 1 + 2*sin(x)$ over the interval $\displaystyle [0,2Pi)$

Factored with the quadratic to get:

$\displaystyle sin(x) = (1+sqrt(3))/2 $

and

$\displaystyle sin(x) = (1-sqrt(3))/2$

But now I'm stuck - I've tried to apply sum/difference rules since 1/2 and sqrt(3)/2 are common values but still no luck.

Any Ideas??

Whit