  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 ground-state 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 spin-wave expansion results. Finally,
having at our disposal improved experimental results for the in-plane spin-wave
dispersion in high-$T_c$ copper oxide $\mbox{La}_2\mbox{CuO}_4$, 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.
