Answer: The formula for sin2θ is sin2θ = 2sinθcosθ. We know that sinθ = 2/3. To evaluate cosθ, we use the fact that in the second quadrant, cosθ is negative. Therefore, cosθ = -sqrt(1-sin2θ). Plugging in the value of sinθ and simplifying, we get cosθ = -sqrt(7/9).
Finally, we can substitute the values of sinθ and cosθ into the formula for sin2θ to get: sin2θ = 2(2/3)(-sqrt(7/9)) = -4/3.