$\text{ The point }A(\sin \theta ,\cos \theta )\text{ is }3\text{ units away from the point }B\left(2\cos {75}^{\circ },2\sin {75}^{\circ }\right)\text{ if }{0}^0\le \theta <{360}^{\circ }\text{ then }\theta =$

$\sqrt{(2\cos 75-\sin \theta {)}^2+(2\sin 75-\cos \theta {)}^2}=3$

$4\left({\cos }^{2}75+{\sin }^{2}75\right)+{\sin }^2\theta +$${\cos }^2\theta -4(\sin \theta \cos 75+\cos \theta \sin 75)=9$

$\Rightarrow \sin (\theta +75)=-1=\sin {270}^{\circ }$

$\Rightarrow \theta +75={270}^0\Rightarrow \theta ={270}^0-{75}^0={195}^0$