The integral ${\int }_{\pi /6}^{\pi /3}{\tan }^{3}x\cdot {\sin }^{2}3x\left(2{\sec }^{2}x\cdot {\sin }^{2}3x+3\tan x.\sin 6x)dx\right.$ is equal to [JEE Main 2020, 4 Sep (Shift 2)]

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The integral \({\int }_{\pi /6}^{\pi /3}{\tan }^{3}x\cdot {\sin }^{2}3x\left(2{\sec }^{2}x\cdot {\sin }^{2}3x+3\tan x.\s…

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