MathNet 2025-part-02 — 186 problems (EN–VI) Question 123

There are $n$ values of $x$ in the interval $0 \lt x \lt 2\pi$ where $f(x) = \sin(7\pi \cdot \sin(5x)) = 0$. For $t$ of these $n$ values of $x$, the graph of $y = f(x)$ is tangent to the $x$-axis. Find $n + t$.