Uniform scale family: a UMP two-sided test exists (misprinted hypotheses)

Let $X_1$ and $X_2$ be iid $U(0,\theta)$. The UMP test of size $\alpha$ to test $H_0:\theta=\theta_1$ against $H_1:\theta\ne\theta_1$ is ($x_{(2)}=\max(X_1,X_2)$; the booklet prints the hypotheses as "$\theta_1=\theta_2$ against $\theta_1\ne\theta_2$"):