  We report the $\mathbf{H}-T$ phase diagram of $S=1/2$ strongly frustrated
anisotropic spin chain material linarite PbCuSO$_4$(OH)$_2$ in tilted magnetic
fields up to 10 T and temperatures down to 0.2 K. By means of torque
magnetometry we investigate the phase diagram evolution as the magnetic field
undergoes rotation in $\mathbf{ba}^{\ast}$ and $\mathbf{bc}$ planes. The key
finding is the robustness of the high field spin density wave-like phase, which
may persist even as the external field goes orthogonal to the chain direction
$\mathbf{b}$. In contrast, the intermediate collinear antiferromagnetic phase
collapses at moderate deflection angles with respect to $\mathbf{b}$ axis.
