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Equations with trigonometry in them can look scary, but that's nothing that a quick little substitution can't fix.

In the domain \( [0, 2\pi] \), how many solutions are there to

\[ \cos 3 \theta = 4 \cos \theta + 3 ? \]

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If provided that \[\sin x+\cos x=\frac{1}{6},\] what is the value of \(\sin 3x-\cos 3x ?\)

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