Evaluate ∫0π/3sin2(θ)cos2(θ)dθ\int_0^{\pi/3} \sin^2(\theta) \cos^2(\theta) d\theta∫0π/3sin2(θ)cos2(θ)dθ using the identity sin(θ)cos(θ)=12sin(2θ)\sin(\theta)\cos(\theta) = \frac{1}{2}\sin(2\theta)sin(θ)cos(θ)=21sin(2θ).
π24−332\frac{\pi}{24} - \frac{\sqrt{3}}{32}24π−323
π12−316\frac{\pi}{12} - \frac{\sqrt{3}}{16}12π−163
π8\frac{\pi}{8}8π
38\frac{\sqrt{3}}{8}83