Find the principal value of `tan^(-1){sin(-pi/2)}`

Explanation

To find the principal value of \( \tan^{-1}(\sin(-\frac{\pi}{2})) \), we can follow these steps:

### Step 1: Evaluate \( \sin(-\frac{\pi}{2}) \)
The sine function is defined as follows:
\[ \sin(-\theta) = -\sin(\theta) \]
Thus, we can calculate:
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