Ultimate Resemblance

Geometry Level 4

{x1y2=a2y1x2=a \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[α,β] a \in [\alpha , \beta ] , then find the value of α+β \alpha + \beta .

This is not my original problem.
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