Analytical formulae for de Haas-van Alphen (dHvA) oscillations in linear chain of coupled two-dimensional (2D) orbits (Pippard's model) are derived systematically taking into account the chemical potential oscillations in magnetic field. Although corrective terms are observed, basic (α) and magnetic breakdown-induced (β and 2βα) orbits can be accounted for by the Lifshits-Kosevich (LK) and Falicov-Stachowiak semiclassical models in the explored field and temperature ranges. In contrast, the 'forbidden orbit' βα amplitude is described by a non-LK equation involving a product of two classical orbit amplitudes. Furthermore, strongly non-monotonic field and temperature dependence may be observed for the second harmonics of basic frequencies such as 2α and the magnetic breakdown orbit β + α, depending on the value of the spin damping factors. These features are in agreement with the dHvA oscillation spectra of the strongly 2D organic metal θ-(ET)4CoBr4(C6H4Cl2).Introduction. -Quasi-two-dimensional (q-2D) multiband organic compounds (ET) 2 X (where ET stands for the bis-ethylenedithio-tetrathiafulvalene molecule and X is a monovalent anion) exhibit very rich phase diagrams with ground states ranging from antiferromagnetic insulator to Fermi liquid. In particular, superconducting and magnetic ordered phases are observed close to each other which is reminiscent of cuprates and iron-based superconductors (for a recent review, see [1] and references therein). These compounds share the same Fermi surface (FS) topology which is an illustration of the linear chain of coupled orbits introduced by Pippard in the early sixties [2]. Such FS is liable to give rise to a network of orbits coupled by magnetic breakdown (MB) in large magnetic fields. Quantum oscillations in such systems have been extensively studied during the two last decades (for a review, see e.g. [3] and references therein). The main feature of the oscillation spectra of these comp-1