Evaluation of definite integrals by subsitiution and properties of its :
If `theta_(1)` and `theta_(2)` be respectively the smallest and the largest values of `theta` in `(0,2pi)-{pi}` which satisfy the equation, `2cot^(2)theta-(5)/(sintheta)+4=0`, then `int_(theta_(1))^(theta_(2))cos^(2)3thetad""theta` is equal to :

Options

A. `(2pi)/(3)`
B. `(pi)/(3)`
C. `(pi)/(3)+(1)/(6)`
D. `(pi)/(9)`

Answer

B