If `A=[costheta-sinthetasinthetacostheta]` , then `A^T+A=I_2` , if `theta=npi,\ \ n in Z` (b) `theta=(2n+1)pi/2,\ \ n in Z` (c) `theta=2n\ pi+pi/3,\ \ n in Z` (d) none of these

Explanation

To solve the problem, we need to determine the values of \( \theta \) for which the matrix \( A \) satisfies the equation \( A^T + A = I_2 \), where \( A = \begin{bmatrix} \cos \theta & -\sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix} \) and \( I_2 \) is the identity matrix of order 2.

### Step-by-step Solution:

1. **Write down the matrix \( A \)**:
\[ A = \begin{bmatrix} \cos \theta & -\sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix} \]
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