Posted by Chiquesta on Saturday, December 17, 2011 at 7:24am.
sin^6θ = (sin^2θ)^3
= (1 - cos^2θ)^3
= 1 - 3cos^2θ + 3cos^4θ + cos^6θ
Now you can use your half-angle formula
cos^2θ = (1 + cos 2θ)/2
to get no exponents and multiples of θ.
You will end up with
1/192 (60θ - 45sin2θ + 9sin4θ - sin6θ)
from 0 to pi/2 yields 30pi/192
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