If the domain of the function \(f\left(x\right)={\text{sin}}^{−1}\left(\frac{1}{{x}^{2}−2x−2}\right)\) is \(\left(−∞,\al…

If the domain of the function \(f\left(x\right)={\text{sin}}^{−1}\left(\frac{1}{{x}^{2}−2x−2}\right)\) is \(\left(−∞,\alpha \left]\cup \right[\beta ,\gamma \left]\cup \right[\delta ,∞\right)\), then \(\alpha +\beta +\gamma +\delta\) is equal to

[JEE Main 2026, 24 Jan (Shift 2)]