To find the length of the curve, we need to compute the arc length integral.
First, we find the derivatives with respect to $t$:
$\frac{dx}{dt} = -24\cos^2 t \sin t$
$\frac{dy}{dt} = 24\sin^2 t \cos t$
Then, we compute the integrand:
$\sqrt{(\frac{dx}{dt})^2 +
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