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If \( \mathrm{n} \) is the number of solutions of the equation \( 2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi] \)
\( \mathrm{P} \)
W) and \( \mathrm{S} \) is the sum of all these solutions, then the ordered \( \operatorname{pair}(\mathrm{n}, \mathrm{S}) \) is
[JEE Main-2021 (September)]
(a) \( \left(3, \frac{13 \pi}{9}\right) \)
(b) \( \left(2, \frac{2 \pi}{3}\right) \)
(c) \( \left(2, \frac{8 \pi}{9}\right) \)
(d) \( \left(3, \frac{5 \pi}{3}\right) \)
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