Trolling Trignometry

Geometry Level 3

\[3\sin(x) + 3\cos(y) + 3\tan(z) + 3\sec(y) + 3\csc(x) + 3\cot(z) + 6\]

Find the minimum value of the expression above for \(x,y,z \in \left(0, \frac \pi 2\right)\).

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