#1**+1 **

First, note that \(\tan({\pi\over4})=1\). Imagine this on the unit circle. Since we need to find \(x\) when its tangent is *negative *1, we have to get to the 2nd and 4th quadrant while retaining the tangent's absolute slope. To do that, we add \(90^o\) or \({\pi\over2}\) and \(270^o\) or \({3\pi\over2}\) to the angle \({\pi\over4}\). When we do that, we get the angles \({3\pi\over4}\) and \({7\pi\over4}\).

Q.E.D.

Mathhemathh
Oct 18, 2017