Trigonometric Identities

Geometry Level 2

Let \(\alpha\) and \(\beta\) be the values of \(\theta\) that satisfy \(\sin \theta + \sqrt{3} \cos \theta = 0\), where \(0 \leq \theta \leq 2\pi\). What is the value of \(\tan^2\left(\alpha + \beta\right)\)?

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