This is an integral for finding length of a segment of a parametric graph.

$\displaystyle \int \sqrt{(\frac{1}{2\sin .5t \cos .5t} - \sin t)^2 + (\cos t)^2}$

I simplified it down to this

$\displaystyle \int |\cot t|$

How do you go about solving this for the interval from $\displaystyle \frac{\pi}{4} to \frac{3\pi}{4}$?