1998 IMO Shortlist Problems/A3

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Let $x,y.z$ be positive real numbers such that $xyz=1$. Prove that $\frac{x^3}{(1+y)(1+z)+\frac{y^3}{(1+x)(1+z)}+\fra{z^3}{(1+x)(1+y)}\geq \frac{3}{4}$ (Error compiling LaTeX. Unknown error_msg)