Question
If $0 < x < {1 \over {\sqrt 2 }}$ and ${{{{\sin }^{ - 1}}x} \over \alpha } = {{{{\cos }^{ - 1}}x} \over \beta }$, then the value of $\sin \left( {{{2\pi \alpha } \over {\alpha + \beta }}} \right)$ is :
If $0 < x < {1 \over {\sqrt 2 }}$ and ${{{{\sin }^{ - 1}}x} \over \alpha } = {{{{\cos }^{ - 1}}x} \over \beta }$, then the value of $\sin \left( {{{2\pi \alpha } \over {\alpha + \beta }}} \right)$ is :