critical and inflection pts

find the critical points of f(x) and use the second derivative test (if possible) to determine whether each corresponds to a max or min.

$\displaystyle f(x)=sin(x)^2+cos(x)$ ,[0,pi]

i got f'(x) and f''(x) but im just having a little trouble setting them equal to zero and solving for the critical and inflection points. Could someone help me out on that please?

$\displaystyle f'(x)=2*sin(x)*cos(x)-sin(x)=0$ x=? -->critical pts.

$\displaystyle f''(x)=4*cos(x)^2-cos(x)-2=0$ x=? -->inflection pts