roots = Reduce[ Sin[z + Sin[z + Sin[z]]] == Cos[z + Cos[z + Cos[z]]] && -3 < Re[z] < 3 && -3 < Im[z] < 3, z] // Quiet;
ListPlot[{Re[z], Im[z]} /. {ToRules[roots]}, PlotLabel -> Style[TraditionalForm[ Sin[z + Sin[z + Sin[z]]] == Cos[z + Cos[z + Cos[z]]]], 14], PlotStyle -> Red, AspectRatio -> 1]