`tantheta-tan(theta/2)=sec(theta/2)`.Then find its general solution

Explanation

To solve the equation \( \tan \theta - \tan \frac{\theta}{2} = \sec \frac{\theta}{2} \), we will follow these steps:

### Step 1: Rewrite the equation using trigonometric identities
We know that:
\[ \tan \theta = \frac{\sin \theta}{\cos \theta} \quad \text{and} \quad \tan \frac{\theta}{2} = \frac{\sin \frac{\theta}{2}}{\cos \frac{\theta}{2}} \quad \text{and} \quad \sec \frac{\theta}{2} = \frac{1}{\cos \frac{\theta}{2}} \]
Substituting these into the equation gives:
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