Small angle neutron scattering experiments were performed on a bulk single crystal of chiral-lattice multiferroic insulator Cu$_2$OSeO$_3$. In the absence of an external magnetic field, helical spin order with magnetic modulation vector $q parallel <001>$ was identified. When a magnetic field is applied, a triple-$q$ magnetic structure emerges normal to the field in the A-phase just below the magnetic ordering temperature $T_c$, which suggests the formation of a triangular lattice of skyrmions. Notably, the favorable $q$-direction in the A-phase changes from $q parallel <110>$ to $q parallel <001>$ upon approaching $T_c$. Near the phase boundary between these two states, the external magnetic field induces a 30$^circ$-rotation of the skyrmion lattice. This suggests a delicate balance between the magnetic anisotropy and the spin texture near $T_c$, such that even a small perturbation significantly affects the ordering pattern of the skyrmions.
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