Math Help - Hopefully last Polar question.

1. Hopefully last Polar question.

Find the argument of :
$1 - cot (\frac{pi}{8})$
The answer is $\frac{-3pi}{8}$

And i have no idea =(...doing cot(pi / 8) gives me some horrible decimal i can't work with...as does tan(pi/8)
Any help would be really appreciated!
Thank-you very much!

2. You can find $1-cot(\frac{\pi}{8})$ by using the half-angle identity: $cot(\frac{x}{2}) = \frac{1+cos(x)}{sin(x)}$, with $x=\frac{\pi}{4}$. This yields $\frac{2+\sqrt{2}}{\sqrt{2}}$. Subtracting from 1 and simplifying yields $-\sqrt{2}$. As for finding the argument, I'm not sure what you mean, as the argument is usually the angle something makes with the positive x-axis, and $-\sqrt{2}$ is just a number, not a vector.

3. uh is there a way to do this without the half angle identity because i havn't used that before?