The value of `cot((7pi)/16)+2cot((3pi)/8)+cot((15pi)/16)` is (a)`4` (b)` 2` (c) `-2` (d) `-4`

Explanation

To solve the expression \( \cot\left(\frac{7\pi}{16}\right) + 2\cot\left(\frac{3\pi}{8}\right) + \cot\left(\frac{15\pi}{16}\right) \), we will use trigonometric identities and properties of cotangent.

### Step-by-step Solution:

1. **Rewrite Cotangent in Terms of Tangent**:
We know that \( \cot(\theta) = \tan\left(\frac{\pi}{2} - \theta\right) \). Thus, we can rewrite the terms:
\[
\cot\left(\frac{7\pi}{16}\right) = \tan\left(\frac{\pi}{2} - \frac{7\pi}{16}\right) = \tan\left(\frac{8\pi}{16} - \frac{7\pi}{16}\right) = \tan\left(\frac{\pi}{16}\right)
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