7. The sum of all positive integers $n$ that satisfy $\frac{1}{4}<\sin \frac{\pi}{n}<\frac{1}{3}$ is $\qquad$ .
Let $f(x)=\frac{\sin x}{x}, x \in\left(0, \frac{\pi}{6}\right), f^{\prime}(x)=\frac{x \cos x-\sin x}{x^{2}}$. Let $h(x)=x \cos x-\sin x$, then $h^{\prime}(x)=-x \sin x\frac{1}{3}$, so the positive integers $n=10,11,12$ satisfy the condition. In summary, the sum of all positive integers $n$ that satisfy $\frac{1}{4}<\sin \frac{\pi}{n}<\frac{1}{3}$ is 33.