SOLUTION: How do use a half-angle formula to find the exact value of sin 7pie/8 ?

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The half angle formula for sin(theta) is
sin(theta/2) = ± sqrt[(1 - cos(theta)) / 2]
If we know cos(7pi/4) = sqrt(2) / 2, we just plug it in, so we get
sin(7pi/8) = ± sqrt[(1 - sqrt(2)/2) / 2]
(It is clumsy to do trig this way, ya know...)