If `theta` is an acute angle and `tantheta+cottheta=2,` find the value of `tan^7theta+cot^7theta` .

Explanation

To solve the problem, we will follow these steps:

### Step 1: Set up the equation
Given that \( \tan \theta + \cot \theta = 2 \), we can express \( \cot \theta \) in terms of \( \tan \theta \):
\[ \cot \theta = \frac{1}{\tan \theta} \]
Thus, we can rewrite the equation as:
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