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The relevance of the quasi-two-dimensional spin-1/2 frustrated quantum antiferromagnet due to its possibility of modelling the high-temperature superconducting parent compounds has resulted in numerous theoretical and experimental studies. This paper presents a detailed research of the influence of the varying exchange interactions on the model magnetic properties within the framework of self-consistent spin-wave theory based on Dyson-Maleev representation. Beside the nearest neighbour interaction within the plane, the planar frustration up to the third nearest neighbours, cyclic interaction and the interlayer coupling are taken into account. The detailed description of the elementary spin excitations, staggered magnetization, spin-wave velocity renormalization factor and groundstate energy is given. The results are compared to the predictions of the linear spin-wave theory and when possible also to the second-order perturbative spinwave expansion results. Finally, having at our disposal improved experimental results for the in-plane spin-wave dispersion in high-T c copper oxide La 2 CuO 4 , the self-consistent spin-wave theory is applied to that compound in order to correct earlier obtained set of exchange parameters and high temperature spin-wave dispersion. (Milica S. Rutonjski ) interaction, Quasi-two-dimensional antiferromagnetic copper oxides a c x y z J 2 J 3 J c J J Figure 1: (Color online) Magnetic unit cell (bold solid line) of 3D antiferromagnet with exchange interactions labeled. Two different orientations of spins are denoted by open and solid circles.