The set of solutions of the equation $\left(\sqrt{3}-1\right)\sin \theta +\left(\sqrt{3}+1\right)\cos \theta =2$  is

$\frac{\left(\sqrt{3}-1\right)}{2\sqrt{2}}\sin \theta +\frac{\left(\sqrt{3}+1\right)}{2\sqrt{2}}\cos \theta =\frac{2}{2\sqrt{2}}$

$\sin \theta .\sin \frac{\pi }{12}+\cos \theta .\cos \frac{\pi }{12}=\frac{1}{\sqrt{2}}$

$\cos \left(\theta -\frac{\pi }{12}\right)=\cos \frac{\pi }{4}$

$\therefore \theta -\frac{\pi }{12}=2n\pi \pm \frac{\pi }{4}$

$\theta =2n\pi \pm \frac{\pi }{4}+\frac{\pi }{12}$

$\left\{2n\pi \pm \frac{\pi }{4}+\frac{\pi }{12}:n\in z\right\}$