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We examine interplay between spin density wave (SDW) and the putative Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in CeCoIn₅. We use thermal conductivity measurement along a-axis in magnetic field applied at various angles away from the c-axis within the bc plane of this tetragonal compound. We compare our results to those of our theoretical model which shows that SDW state in CeCoIn₅ is stabilized when the field is directed close to the ab plane. The SDW phase disappears when the field is rotated away from the ab plane.When the field is rotated toward the c axis, the FFLO state emerges while the SDW phase disappears. As a function of field, we observed the reduction of thermal conductivity for field close to the ab plane and the enhancement of thermal conductivity when field is close to the c axis, consistent with the theoretical expectations of additional contribution to the heat transpot from the FFLO nodal planes.