Maximum Value

Geometry Level 4

\[\left(\sin x\right) \left(\sin^3 x + 3\right) + \left(\cos x\right) \left(\cos^3 x + 4\right) + \frac{\sin^2 2x}2 + 4\cos x + 5\]

What is the maximum value of the expression above? Give your answer to 3 decimal places.

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