It isn't as complicated as it looks

Algebra Level 4

1(1x)(1y)(1z)+1(1+x)(1+y)(1+z)\large \frac{1}{(1-x)(1-y)(1-z)}+\frac{1}{(1+x)(1+y)(1+z)} For 1<x,y,z<1-1<x,y,z<1, let tt denote the minimum value of the above expression and uu be the sum of x,y,zx,y,z when the equality holds, find (3t)u+4(3t)^{u}+4.

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