Min + Max? (Trigonometry)

Geometry Level 4

Given that \(\sin ^{ 2 }{ x } +\sin ^{ 2 }{ y } =\dfrac 12 \). Let \(m\) and \(M\) denote the minimum value and maximum value, respectively, of \(S=\tan ^{ 2 }{ x } +\tan ^{ 2 }{ y } \), find \(m+M\).

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