Does there exist real number $\theta\in \mathbb{R}$\ $\mathbb{Q}$ such that Irrationality Measure of $\theta$ is itself?
$$\forall \epsilon >0, \exists C>0, \forall(p,q)\in \mathbb{Z^2},\bigg|\theta-\frac{p}{q} \bigg|\geq\frac{C}{q^{\theta+\epsilon}}$$