Prove that: `t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha`

Explanation

To prove that \( \tan \alpha + 2 \tan 2\alpha + 4 \tan 4\alpha + 8 \cot 8\alpha = \cot \alpha \), we will start from the left-hand side (LHS) and manipulate it step by step.

### Step 1: Write down the LHS
We start with the left-hand side:
\[ LHS = \tan \alpha + 2 \tan 2\alpha + 4 \tan 4\alpha + 8 \cot 8\alpha \]

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