Two Zeros of a Maximum

Let $f(x) = \sin \pi x$ and $g(x) = -x^2 + 2ax - a^2 + 1$. Writing $\max\{a, b\}$ for the larger of $a$ and $b$, define

If $M(x)$ has exactly two zeros in the interval $(0, 2)$, find the range of possible values of the real number $a$.