# 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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