Answer
$\sin{255^o}=-\dfrac{\sqrt6+\sqrt2}{4}$
Work Step by Step
Note that $255^o=210^o+45^o$.
Hence, the given expression is equivalent to $\sin(210^o+45^o)$.
RECALL:
$\sin{(A+B)}=\sin{A}\cos{B}+\cos{A}\sin{B}$
Use the identity above with $A=210^o$ and $B=45^o$ to obtain:
\begin{align*}
\sin{255^o}&=\sin{(210^o+45^o)}\\\\
&=\sin{210^o}\cos{45^o}+\cos210^o\sin45^o\\\\
&=\left(-\frac{1}{2}\right)\left(\frac{\sqrt2}{2}\right)+\left(-\frac{\sqrt3}{2}\right)\left(\frac{\sqrt2}{2}\right)\\\\
&=-\frac{\sqrt2}{4}+\left(-\frac{\sqrt6}{4}\right)\\\\
&=-\dfrac{\sqrt6+\sqrt2}{4}
\end{align*}