The exhaustive set of values of a for which `a - cot^(-1) 3x = 2 tan^(-1) 3x + cos^(-1) x sqrt3 + sin^(-1) x sqrt3` may have solution, is
A. `[-(pi)/(4), (pi)/(4)]`
B. `((pi)/(2), (3pi)/(2))`
C. `[(2pi)/(3), (4pi)/(3)]`
D. `[-(3pi)/(6), (7pi)/(6)]`

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