# Trigonometry Related Part III

Geometry Level 5

$\frac{a}{1+a^2}+\frac{b}{1+b^2}+\frac{3c}{\sqrt{1+c^2}}$

Given that $$a,b$$ and $$c$$ are positive real numbers satisfying $$ab+bc+ca=1$$.

If the maximum value of the expression above can be expressed as $$\sqrt{M}$$ for positive integer $$M$$, determine $$M$$.

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