3. Given $f(x)=\sin (x+\theta)+\sqrt{3} \cos (x+\theta)$ is an even function, the value of $\theta$ is equal to


3. $k \pi+\frac{\pi}{3}$.
$f(x)=2 \sin \left(x+\theta+\frac{\pi}{6}\right)$. If $f(x)$ is an even function, then it must be that $\theta+\frac{\pi}{6}=k \pi+\frac{\pi}{2}, \theta=k \pi+\frac{\pi}{3}$.