Phase-alternated compositeπ/2 pulses have been constructed for spinI=1 to overcome quadrupole interaction effects in solid state nuclear magnetic resonance (NMR) spectroscopy. Magnus expansion approach is used to design these sequences in a manner similar to the NMR coherent averaging theory. It is inferred that the symmetric phase-alternated compositeπ/2 pulses reported here are quite successful in producing quadrupole echo free from phase distortions. This effectiveness of the present composite pulses is due to the fact that most of them are of shorter durations as compared to the ones reported in literature. In this theoretical procedure, irreducible spherical tensor operator formalism is employed to simplify the complexity involved in the evaluation of Magnus expansion terms. It has been argued in this paper that compositeπ/2 pulse sequences for this purpose can also be derived from the broadband inversionπ pulses which are designed to compensate electric field gradient (efg) inhomogeneity in spinI=1 nuclear quadrupole resonance (NQR) spectroscopy.