Let the domains of the functions \(\mathrm{f}(\mathrm{x})=\log _4 \log _3 \log _7\left(8-\log _2\left(\mathrm{x}^2+4 \ma…

Let the domains of the functions \(\mathrm{f}(\mathrm{x})=\log _4 \log _3 \log _7\left(8-\log _2\left(\mathrm{x}^2+4 \mathrm{x}+5\right)\right)\) and \(\mathrm{g}\left(\mathrm{x}\right)={\sin }^{-1}\left(\frac{7\mathrm{x}+10}{\mathrm{x}-2}\right)\) be \((\alpha ,\beta )\) and \([\gamma ,\delta ]\), respectively. Then \({\alpha }^{2}+{\beta }^{2}+{\gamma }^{2}+{\delta }^{2}\) is equal to:-

[JEE Main 2025, 4 Apr (Shift 2)]