\cos(4\theta) - 4\sin^2 \theta = 2(\cos(2\theta) + \frac{ 1 }{ 2 })^2 + \frac{ 7 }{ 2 }\cos(4\theta) - 4\sin^2 \theta = 2(\cos(2\theta) + \frac{ 1 }{ 2 })^2 + \frac{ 7 }{ 2 }

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