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

Explanation

To solve the problem, we need to find the value of \( \alpha + \beta \) given the conditions \( \cot \alpha = \frac{1}{2} \) and \( \sec \beta = -\frac{5}{3} \), with the ranges \( \frac{3\pi}{2} < \alpha < 2\pi \) and \( \frac{\pi}{2} < \beta < \pi \).

### Step 1: Find \( \tan \alpha \)
Given \( \cot \alpha = \frac{1}{2} \), we can find \( \tan \alpha \) as follows:
\[ \tan \alpha = \frac{1}{\cot \alpha} = 2 \]

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