# Sole Constraint

Algebra Level 4

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

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