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We consider a one-dimensional photonic crystal composed of alternating layers of isotropic and anisotropic dielectric materials. Such a system has different band structures for different polarizations of light. We demonstrate that if a defect layer is inserted into the structure, the crystal can support a polarized optical defect mode that is a bound state in the continuum (BIC). In the case of an anisotropic defect layer, by tilting the principle dielectric axes of the defect layer relative to those of the photonic crystal the BIC is transformed to a quasi-BIC. We derive an analytical expression for the decay rate of the resonance. An experimental setup with a liquid crystal defect layer is proposed to tune the factor of the quasi-BIC through applying an external electric field. We speculate that the setup provides a simple and robust platform for observing optical bound states in the continuum in the form of resonances with tunable  …