If roots of equation `3x^(2) + 5x + 1 = 0` are `(sectheta_(1) - tentheta_(1)) and (cosectheta_(2)-cottheta_(2)),` then find the equation whose roots are `(sectheta_(1)+tantheta_(1) and (cosectheta_(2) + cottheta_(2)).`

Explanation

To find the equation whose roots are \( \sec \theta_1 + \tan \theta_1 \) and \( \csc \theta_2 + \cot \theta_2 \), we start with the given equation \( 3x^2 + 5x + 1 = 0 \) whose roots are \( \sec \theta_1 - \tan \theta_1 \) and \( \csc \theta_2 - \cot \theta_2 \).

### Step 1: Identify the roots of the original equation
The roots of the equation \( 3x^2 + 5x + 1 = 0 \) are:
- \( \alpha = \sec \theta_1 - \tan \theta_1 \)
- \( \beta = \csc \theta_2 - \cot \theta_2 \)

### Step 2: Use the reciprocal relationship
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