$2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1$

$2 \cos x\left(4\left(\sin ^{2} \frac{\pi}{4}-\sin ^{2} x\right)-1\right)=1$

$2 \cos x\left(4\left(\frac{1}{2}-\sin ^{2} x\right)-1\right)=1$

$2 \cos x\left(2-4 \sin ^{2} x-1\right)=1$

$2 \cos x\left(1-4 \sin ^{2} x\right)=1$

$2 \cos x\left(4 \cos ^{2} x-3\right)=1$

$4 \cos ^{3} x-3 \cos x=\frac{1}{2}$

$\cos 3 x=\frac{1}{2}$

$\mathrm{x} \in[0, \pi] \therefore 3 \mathrm{x} \in[0,3 \pi]$