Answer
$-\dfrac {\sqrt {2}}{4}\left( \sqrt {3}+1\right) $
Work Step by Step
$\sin \left( 255\right) =\sin \left( 225+30\right) =\sin {225}\cos 30+\cos 225\sin 30=-\dfrac {\sqrt {2}}{2}\dfrac {\sqrt {3}}{2}-\dfrac {\sqrt {2}}{2}\dfrac {1}{2}=-\dfrac {\sqrt {2}}{4}\left( \sqrt {3}+1\right) $