If $A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$, then find the value of $\theta$ satisfying the equation $A^T + A = I_2$

Question

$(A)\; \theta = 2 n \pi +\frac{\pi}{3}$
$(B)\; \theta = 2 n \pi -\frac{\pi}{3}$
$(C)\; \theta = 2 n \pi \pm \frac{\pi}{3}$
$(D)\; \theta = 2n\pi$