If `cotalpha=1/2`,`secbeta=-5/3`,where `piltalphalt(3pi)/2`and `pi/2 ltbetaltpi`.find the value of `alpha + beta` terminates

Explanation

To find the value of \( \alpha + \beta \) given \( \cot \alpha = \frac{1}{2} \) and \( \sec \beta = -\frac{5}{3} \), where \( \frac{3\pi}{2} < \alpha < 2\pi \) and \( \frac{\pi}{2} < \beta < \pi \), we can follow these steps:

### Step 1: Determine the angle \( \alpha \)

Given \( \cot \alpha = \frac{1}{2} \), we can use the definition of cotangent, which is the ratio of the adjacent side to the opposite side in a right triangle.

Let:
- Opposite side = 1
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