find value of the expression

[fibonacci]

If $ x,y,z$ real positive numbers such that $ x+y+z+\sqrt{xyz} =4$ , then find value of the expression:
$ \sqrt{(4-x)(4-y)z} + \sqrt{(4-y)(4-z)x} + \sqrt{(4-z)(4-x)y} - \sqrt{xyz} $

[Rak so dna]

$ \sqrt{(4-x)(4-y)z} + \sqrt{(4-y)(4-z)x} + \sqrt{(4-z)(4-x)y} - \sqrt{xyz} =$ $(4-x-y+z)+(4+x-y-z)+(4-x+y-z)-(4-x-y-z) = 8 $

[fibonacci]

А я использовало $x=4cos^2a...$