1. The problem asks for the value of the angle $\theta$ when both $x$ and $y$ coordinates are negative. 2. In the Cartesian coordinate system, the angle $\theta$ is typically measured from the positive $x$-axis to the point $(x,y)$. 3. When both $x$ and $y$ are negative, the point lies in the third quadrant. 4. The angle $\theta$ in the third quadrant can be found using the formula: $$\theta = 180^\circ + \arctan\left(\frac{y}{x}\right)$$ or in radians: $$\theta = \pi + \arctan\left(\frac{y}{x}\right)$$ 5. This is because $\arctan\left(\frac{y}{x}\right)$ gives an angle in the first or fourth quadrant, so adding $180^\circ$ (or $\pi$ radians) shifts it to the third quadrant. 6. Therefore, if $x<0$ and $y<0$, the angle $\theta$ is between $180^\circ$ and $270^\circ$ (or between $\pi$ and $\frac{3\pi}{2}$ radians). 7. In summary, the value of $\theta$ when both $x$ and $y$ are negative is: $$\theta = 180^\circ + \arctan\left(\frac{y}{x}\right)$$ or $$\theta = \pi + \arctan\left(\frac{y}{x}\right)$$ This locates the angle correctly in the third quadrant.