For the function $f(x) = \sin\frac{\pi}{4}x$, find the sum of all natural numbers $x$ satisfying the inequality $$f(2+x)f(2-x) < \frac{1}{4}$$ for $0 < x < 16$. [3 points]
For the function $f(x) = \sin\frac{\pi}{4}x$, find the sum of all natural numbers $x$ satisfying the inequality
$$f(2+x)f(2-x) < \frac{1}{4}$$
for $0 < x < 16$. [3 points]