Determine the principle value of the argument

-1-i

tan($\displaystyle \theta$) = -1/-1 = $\displaystyle \frac{\pi}{2}$ but it is negative because it is in the 4th quadrant

the answer is $\displaystyle \frac{-3\pi}{4}$

Principle Argument is simple the argument except between the values of $\displaystyle -\pi $and $\displaystyle \pi$

What did i do wrong?