For any $y\in \mathrm{ℝ}$, let ${\cot }^{-1}(y)\in (0,\pi )$ and ${\tan }^{-1}(y)\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ Then the sum of all the solutions of the equation ${\tan }^{-1}\left(\frac{6y}{9-{y}^{2}}\right)+{\cot }^{-1}\left(\frac{9-{y}^{2}}{6y}\right)=\frac{2\pi }{3}$ for $0

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For any $y\in \mathrm{ℝ}$, let ${\cot }^{-1}(y)\in (0,\pi )$ and ${\tan }^{-1}(y)\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ Then the sum of all the solutions of the equation ${\tan }^{-1}\left(\frac{6y}{9-{y}^{2}}\right)+{\cot }^{-1}\left(\frac{9-{y}^{2}}{6y}\right)=\frac{2\pi }{3}$ for $0<|y|<3$, is equal to: [JEE Advanced 2023]

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For any \(y\in \mathrm{ℝ}\), let \({\cot }^{-1}(y)\in (0,\pi )\) and \({\tan }^{-1}(y)\in \left(-\frac{\pi }{2},\frac{\p…

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