Asymptotic estimate on minimum of a function

Question

Let $$V(x) = 2 - \sin(2\pi x) - \sin(2\pi\sqrt{2} x)$$ for $x\in \mathbb{R}$. For each $r>0$, let $$a_r = \min\{a>0: V(a)=r\}$$ We can see that $$ r = V(a_r) = \min\{V(x): x\in [0,a_r]\}$$ I want to estimate (if any) grownth rate of $$ a_r \leq Cr^{-\theta}.$$ Is there any way to do that?