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Let N be the number of triplets (x, y, ...

Let N be the number of triplets `(x, y, z)` where `x, y, z in [0, 2pi]` satisfying the inequality `(4 + sin 4x) (2 + cot^2 - y) (1 + sin ^4+ z) < 12 sin ^2 - z.` Find the value of `N/2.`

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