11 If the function $f(x)=\sin (x+\theta)+\sqrt{3} \cos (x-\theta)$ is an even function, then $\theta=$
$11 k \pi-\frac{\pi}{6}, k \in \mathbf{Z}$. From $f(x)=f(-x)$ we get $\sin (x+\theta)+\sin (x-\theta)=\sqrt{3}[\cos (x+\theta)-\cos (x-\theta)]$, simplifying yields $\tan \theta=-\frac{1}{\sqrt{3}}, \theta=k \pi-\frac{\pi}{6}, k \in \mathbf{Z}$.