Find the principal solutions of the following equations :
(1) `tanx=-sqrt(3)`
(2) `sqrt(3)sec x+2=0`.

Explanation

To find the principal solutions of the given equations, we will solve each equation step by step.

### Part (1): Solve `tan(x) = -√3`

1. **Identify the angle whose tangent is √3**:
- We know that \( \tan(\frac{\pi}{3}) = \sqrt{3} \).

2. **Determine the quadrants where tangent is negative**:
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