упростить 2cos (x+pi/4)cos (2x+pi/4)+sin3x

Решите задачу:

$2cos(x+\frac{\pi}{4})cos(2x+\frac{\pi}{4})+sin(3x)=\\ 2(cosxcos\frac{\pi}{4}-sin xsin \frac{\pi}{4})(cos(2x)cos\frac{\pi}{4}-sin(2x)sin\frac{\pi}{4})+sin(3x)=\\ 2(\frac{\sqrt{2}}{2}cosx-\frac{\sqrt{2}}{2}sin x)(\frac{\sqrt{2}}{2}cos(2x)-\frac{\sqrt{2}}{2}sin(2x))+sin(3x)=\\ 2*\frac{\sqrt{2}}{2}*\frac{\sqrt{2}}{2}(cosx-sin x)(cos(2x)-sin(2x))+sin(3x)=\\ cosxcos(2x)+sinxsin(2x)-(cos(2x)sin x+cosxsin (2x))+sin (3x)=\\ cos(x-2x)-sin(2x+x)+sin(3x)=\\ cos(-x)-sin (3x)+sin(3x)=cos x$