Ultimate Resemblance

Geometry Level 4

\[ \large{\begin{cases} {x \sqrt{1-y^2} = a^2} \\ { y \sqrt{1-x^2} =a } \end{cases} } \]

If the system of equations above have a real solution if and only if \( a \in [\alpha , \beta ] \), then find the value of \( \alpha + \beta \).

This is not my original problem.
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