Positive reals $x,y,z$ are such that: $x+y+z+\sqrt { xyz } =4.$

What is the value of $\sqrt { x\left( 4-y \right) \left( 4-z \right) } +\sqrt { y\left( 4-z \right) \left( 4-x \right) } +\sqrt { z\left( 4-x \right) \left( 4-y \right) } -\sqrt { xyz }?$

The answer is 8.

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