Find all real $x$ in the interval $[0, 2\pi)$ such that \[27 \cdot 3^{3 \sin x} = 9^{\cos^2 x}.\]
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Tags: trigonometry, algebra proposed, algebra
Find all real $x$ in the interval $[0, 2\pi)$ such that \[27 \cdot 3^{3 \sin x} = 9^{\cos^2 x}.\]