When calculating the voltage in an AC Circuit, I get a different angle from the correct answer
Your solution is correct, the given "correct" answer is wrong. The voltage \$v_2\$ in complex form turns out to be

$$v_2=-0.0095443 + 0.0022665i$$

which is in the second quadrant (negative real part, positive imaginary part). If you just take the arctangent of the imaginary part divided by the real part, then you actually get the angle of \$-v_2\$. This is what the one who computed the "correct" solution must have done. What you (or your software) did, is correct. The angle of \$v_2\$ is given by

$$\arg(v_2)=\arctan\left(\frac{0.0022665}{-0.0095443}\right)\color{red}{+\pi}$$

The addition of \$\pi\$ in this case is done automatically by the function atan2.