Answer
$\frac{\sqrt 6-\sqrt 2}{4}$
Work Step by Step
$sin(165^\circ)=sin(120^\circ+45^\circ)=sin(120^\circ)cos(45^\circ)+cos(120^\circ)sin(45^\circ)=(\frac{\sqrt 3}{2})(\frac{\sqrt 2}{2})+(-\frac{1}{2})(\frac{\sqrt 2}{2})=\frac{\sqrt 6-\sqrt 2}{4}$