Inverse Trigonometric Functions · Medium problem

A student wants the direction angle $\theta$ of the vector $\langle -3,-4\rangle$, measured counterclockwise from the positive $x$-axis with $0\le\theta<2\pi$. She computes $\arctan\dfrac{-4}{-3}=\arctan\dfrac43$ on her calculator. Find the exact value of $\theta-\arctan\dfrac{4}{3}$.