If \(y(x)={\cot }^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right),x\in \left(\f…

If \(y(x)={\cot }^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right),x\in \left(\frac{\pi }{2},\pi \right)\), then \(\frac{dy}{dx}\) at \(x=\frac{5\pi }{6}\) is:

[JEE Main 2021, 27 Aug (Shift 2)]