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 1: Rewrite Secant in Terms of Cosine
We know that \(\sec x = \frac{1}{\cos x}\). Therefore, we can rewrite each secant term in the expression:

\[ 1 + \sec 2\theta = 1 + \frac{1}{\cos 2\theta} = \frac{\cos 2\theta + 1}{\cos 2\theta} \]
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