If the middle term of \(\left(\frac{1}{x}+x \sin x\right)^{10}\)is equal to \(7\frac{7}{8}\) , then value of x is

1
\(\rm 2n\pi + \frac{\pi}{6}\)
2
\(\rm n\pi + \frac{\pi}{6}\)
3
\(\rm n\pi +(-1)^n \frac{\pi}{6}\)
4
\(\rm n\pi +(-1)^n \frac{\pi}{3}\)

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