The value of `f(x)=x^4+4x^3+2x^2-4x+7,` when `x=cot((11pi)/8)` is _________

Explanation

To find the value of the function \( f(x) = x^4 + 4x^3 + 2x^2 - 4x + 7 \) when \( x = \cot\left(\frac{11\pi}{8}\right) \), we will follow these steps:

### Step 1: Simplify \( \cot\left(\frac{11\pi}{8}\right) \)
First, we need to simplify \( \cot\left(\frac{11\pi}{8}\right) \):
\[ \cot\left(\frac{11\pi}{8}\right) = \cot\left(\pi + \frac{3\pi}{8}\right) \]
In the third quadrant, cotangent is positive, so:
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