`tan20^@+tan40^@+sqrt3 tan20^@ tan40^@=` `a.sqrt3/4, b. sqrt3/2, c. sqrt3, d. 1`

Explanation

To solve the problem \( \tan 20^\circ + \tan 40^\circ + \sqrt{3} \tan 20^\circ \tan 40^\circ \), we can use the identity for the tangent of a sum of angles.

### Step-by-Step Solution:

1. **Recognize the Sum of Angles**:
We know that \( \tan(60^\circ) = \tan(40^\circ + 20^\circ) \).

2. **Apply the Tangent Addition Formula**:
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