If \( \mathrm{n} \) is the number of solutions of the equation \( 2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin…

If \( \mathrm{n} \) is the number of solutions of the equation \( 2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1 \), \( x \in[0, \pi] \) and \( \mathrm{S} \) is the sum of all these solutions, then the ordered pair \( (n, S) \) is

[JEE Main 2021, 1 Sep (Shift 2)]