Sole Constraint

Algebra Level 4

Let a,b,a,b, and cc be non-negative real numbers which satisfy 1a2+1+1b2+1+1c2+1=2.\frac{1}{a^{2}+1}+\frac{1}{b^{2}+1}+\frac{1}{c^{2}+1}=2. Find the maximum value of ab+bc+ca.ab+bc+ca.

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