2017 AMC 12A 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) \qquad \textbf{(B)}\ (1, 2) \qquad\textbf{(C)}\ (2, 3) \qquad\textbf{(D)}\ (3, 4) \qquad\textbf{(E)}\ (4,5)

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.