Find the minimum value of `(2-a-4 sec theta)^(2)+(a-3 tan theta)^(2), a in R.`

Explanation

To find the minimum value of the expression \( (2 - a - 4 \sec \theta)^2 + (a - 3 \tan \theta)^2 \), we can follow these steps:

### Step 1: Define the function
Let \( f(\theta, a) = (2 - a - 4 \sec \theta)^2 + (a - 3 \tan \theta)^2 \).

### Step 2: Identify points
We can interpret the expression as the square of the distance between two points:
- Point \( P \) at coordinates \( (2 - a, a) \)
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