Find the exact value of sin 345

$$sin345=sin(120+225)\\\\ =sin120cos225+cos120sin225\\\\ =sin60\times-cos45+-cos60\times-sin45\\\\ =\left(-\frac{\sqrt3}{2}\times\frac{1}{\sqrt2}\right)+\left(\frac{1}{2}\times\frac{1}{\sqrt2}\right)\\\\ =\frac{1-\sqrt3}{2\sqrt2}\\\\ =\frac{(1-\sqrt3)\sqrt2}{4}\\\\ =\frac{\sqrt2-\sqrt6}{4}\\\\$$

Thank you Melody!