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One of the general solutions of $\sqrt{3} \cos θ - 3 \sin θ = 4 \sin 2 θ \cos 3 θ$ is

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$n π + π / 18, n \in Z$

$n π / 2 + π / 6, \forall n \in Z$

$n π / 3 + π / 18, n \in Z$

$\frac{n π}{3} + \frac{π}{9}, n \in Z$

answer is C.

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Detailed Solution

$We have \sqrt{3} \cos θ - 3 \sin θ = 2 (\sin 5 θ - \sin θ)$

$or \cos (θ + π / 6) = \sin 5 θ = \cos (π / 2 - 5 θ)$

$\Rightarrow θ = (n π / 3) + (π / 18)$

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