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The problem in the image is:
\[ 2 \tan \theta = 1 \]

To find the value of the angle \(\theta\), we can follow these steps:

### Step 1: Solve for \(\tan \theta\)
\[
\tan \theta = \frac{1}{2}
\]

### Step 2: Find \(\theta\) using the arctangent function
\[
\theta = \arctan\left(\frac{1}{2}\right)
\]

### Step 3: Calculate \(\theta\)
Using a calculator, we find:
\[
\theta \approx 26.57^\circ
\]

### Step 4: Round to the nearest degree
\[
\theta \approx 27^\circ
\]

So, the angle \(\theta\) is approximately \(27^\circ\) when rounded to the nearest degree.

Would you like more details or have any questions?

Here are five related questions you might find useful:
1. What is the general solution for \(\tan \theta = \frac{1}{2}\)?
2. How does the tangent function behave across different quadrants?
3. How can we find \(\theta\) if given \(\tan \theta = -\frac{1}{2}\)?
4. What is the relationship between the tangent function and the sine and cosine functions?
5. How would you solve the equation if it was \(2 \cot \theta = 1\) instead?

**Tip:** Always double-check your calculator settings (degrees vs radians) when solving trigonometric problems to avoid errors.

Find the value of the angle θ in each of these: 2 tan(θ) = 1. Give each angle correct to the nearest degree.

Learn how to solve the trigonometric equation 2 tan(θ) = 1 and find the angle θ to the nearest degree. This solution involves key trigonometric concepts and the use of the arctangent function, suitable for students in Grades 10-12.

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