Solve equation for values between o and 2 pi
2cos2A + 1 + sinA = 0
use the identity:
$\displaystyle \cos{2\theta} = 1 - 2\sin^{2}{\theta}$
Then try to rearrange the equation as necessary for factoring. If need be, use quadratic formula:
$\displaystyle x = \frac{-b\pm \sqrt{b^2 - 4ac}}{2a}$
EDIT: You may also use $\displaystyle \cos^2{\theta} + \sin^2{\theta} = 1$