Prove that:`tan6^0tan42^0tan66^0tan78^0=1.`

Explanation

To prove that \( \tan 6^\circ \tan 42^\circ \tan 66^\circ \tan 78^\circ = 1 \), we can use the properties of trigonometric functions and some identities. Let's break down the proof step by step.

### Step 1: Rewrite the Tangent Functions
We start by rewriting the tangent functions in terms of sine and cosine:
\[ \tan 6^\circ = \frac{\sin 6^\circ}{\cos 6^\circ}, \quad \tan 42^\circ = \frac{\sin 42^\circ}{\cos 42^\circ}, \quad \tan 66^\circ = \frac{\sin 66^\circ}{\cos 66^\circ}, \quad \tan 78^\circ = \frac{\sin 78^\circ}{\cos 78^\circ} \]
Thus, we can express the product as:
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