Select all expressions matching the value of the definite integral int _(pi /6)^pi /3(dx)/(sin^2)x 3 I (2sqrt (3))/(3) (2)/(sqrt (3)) -(2sqrt (3))/(3)

To solve the definite integral , we can use the substitution method.Let , then . Since , we have . Rearranging, we get .Now, we can rewrite the integral as: This integral can be evaluated using the standard integral .Evaluating this integral from to , we get: Substituting the limits, we have: Simplifying this expression, we get: Therefore, the correct answer is .