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.