If $|5\sin \theta +3\sin (\theta -\frac{\pi }{3})|\le a$ for all  $\theta$ then the least value of a is___

$=5\sin \theta +3(\sin \theta \frac{1}{2}-\cos \theta \frac{\sqrt{3}}{2})$

$=\frac{13}{2}\sin \theta -\frac{3\sqrt{3}}{2}\cos \theta$

Maximum value  $=\sqrt{{\left(\frac{13}{2}\right)}^2+{\left(\frac{3\sqrt{3}}{2}\right)}^2}$

$=\sqrt{\frac{169}{4}+\frac{27}{4}}=\sqrt{\frac{196}{4}}$

$=\frac{14}{2}=7$

$\therefore |5\sin \theta +3\sin (\theta -\frac{\pi }{3})|\le 7$

Least Value of a is 7