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We are given the equation \(\tan 70^\circ = \cot \theta\), and we are asked to find the value of \(\theta\).

### Step 1: Using the identity
Recall that \(\cot \theta\) is the reciprocal of \(\tan \theta\), meaning:
\[
\cot \theta = \frac{1}{\tan \theta}
\]
Thus, the given equation becomes:
\[
\tan 70^\circ = \frac{1}{\tan \theta}
\]

### Step 2: Solving for \(\theta\)
We can now rewrite the equation as:
\[
\tan \theta = \frac{1}{\tan 70^\circ}
\]
Using the fact that \(\tan 70^\circ\) is approximately 2.747, we can find the reciprocal:
\[
\tan \theta = \frac{1}{2.747} \approx 0.364
\]

### Step 3: Inverse tangent
Now, find \(\theta\) using the inverse tangent (\(\tan^{-1}\)) of 0.364:
\[
\theta = \tan^{-1}(0.364)
\]
This gives approximately:
\[
\theta \approx 20^\circ
\]

Thus, the value of \(\theta\) is \(\boxed{20^\circ}\), which corresponds to option C.

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Would you like further details or have any questions?

### Related questions:
1. How does the reciprocal identity relate \(\tan\) and \(\cot\)?
2. How can we approximate values of trigonometric functions without a calculator?
3. What are the key trigonometric identities for solving similar problems?
4. Can \(\theta\) take any other values under different conditions?
5. What are the applications of cotangent and tangent functions in real-world problems?

**Tip:** Always double-check the unit of angles (degrees or radians) when using trigonometric identities.

Learn how to solve the trigonometric equation tan 70° = cot θ using the reciprocal identity and inverse tangent theorem. This step-by-step guide explains the key concepts of trigonometry and is suitable for high school students in Grades 10-12.

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