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1. Sum of variables in a month-length equation ●●●○○ 50 ptsLet $x$, $y$, $z$ be natural numbers satisfying $29x+30y+31z=366$. Find $x+y+z$.
2. Removable sine factors keeping natural roots ●●●○○ 50 ptsThe left-hand side of the equation $\sin \frac{\pi}{x} \sin \frac{2\pi}{x} \sin \frac{3\pi}{x} \cdots \sin \frac{2015\pi}{x}=0$ is a product of factors $\sin \frac{n\pi}{x}$ for $n=1,2,\ldots,2015$. What is the maximum number of these factors that can be crossed out so that the number of natural-number roots of the equation does not change?