If `z=1/(1-cos theta-i sin theta),` then `Re(z)` is a. `0` b. `1/2` c. `cot(theta/2)` d. `1/2 cot (theta/2)`

Explanation

To find the real part of the complex number \( z = \frac{1}{1 - \cos \theta - i \sin \theta} \), we will follow these steps:

### Step 1: Multiply by the Conjugate
To simplify \( z \), we multiply the numerator and the denominator by the conjugate of the denominator:

\[ z = \frac{1}{1 - \cos \theta - i \sin \theta} \cdot \frac{1 - \cos \theta + i \sin \theta}{1 - \cos \theta + i \sin \theta} \]
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