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

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