  We present combined experimental and theoretical investigation of the
low-frequency ESR dynamics in the ordered phases of magnetic mineral linarite.
This material consists of weakly coupled spin-1/2 chains of copper ions with
frustrated ferro- and antiferromagnetic interactions. In zero magnetic field,
linarite orders into a spiral structure and exhibits a peculiar magnetic phase
diagram sensitive to the field orientation. The resonance frequencies and their
field dependence are analyzed combining microscopic and macroscopic theoretical
approaches and precise values of magnetic anisotropy constants are obtained. We
conclude that possible realization of exotic multipolar quantum states in this
material is greatly influenced by the biaxial anisotropy.
