Question

cos(2theta+pi/3)=-radical(3)/2

Answer 1

\[
\cos\left(2\theta+{\pi\over3}\right)={\sqrt{3}\over2}
\]
this happens when
\[2\theta+\frac{\pi}{3}={\pi\over6}+n\pi\\
2\theta=n\pi-{\pi\over6}\\
\theta=n{\pi\over2}-{\pi\over12}
\]

Answer 2

if you have the domain of theta, use the appropriate value for "n"