AMC 12 2017a Problem 15

Let $f(x) = \sin{x} + 2\cos{x} + 3\tan{x}$, using radian measure for the variable $x$. In what interval does the smallest positive value of $x$ for which $f(x) = 0$ lie?

\textbf{(A)}\ (0,1) \textbf{(B)}\ (1, 2) \textbf{(C)}\ (2, 3) \textbf{(D)}\ (3, 4) \textbf{(E)}\ (4,5)