Prove that `(1+sec 2 theta)(1+sec 4 theta)(1+sec 8 theta)=(Tan 8theta)/(tan theta)`

Explanation

To prove that \((1 + \sec 2\theta)(1 + \sec 4\theta)(1 + \sec 8\theta) = \frac{\tan 8\theta}{\tan \theta}\), we will start by simplifying the left-hand side (LHS) step by step.

### Step-by-Step Solution:

1. **Start with the LHS:**
\[ LHS = (1 + \sec 2\theta)(1 + \sec 4\theta)(1 + \sec 8\theta) \]
...