Sets of inhomogeneous linear forms can be not isotropically winning

We give an example of irrational vector $\theta \in {\mathbb{R}}^2$ such that the set $Bad_{\pmb{\theta}} := {(\eta_1,\eta_2): \inf_{x\in$\mathbb{N}$} x^{\frac{1}{2}} \max_{i=1,2} |x \theta_i-\eta_i|>0}$ is not absolutely winning with respect to McMullen’s game.