`sintheta=sqrt(3)/2` and `tantheta=-sqrt(3)`

Explanation

To solve the equations \( \sin \theta = \frac{\sqrt{3}}{2} \) and \( \tan \theta = -\sqrt{3} \), we will find the angles \( \theta \) that satisfy both equations and then determine their general solutions.

### Step 1: Solve \( \sin \theta = \frac{\sqrt{3}}{2} \)

The sine function equals \( \frac{\sqrt{3}}{2} \) at specific angles. We know that:

\[
\sin \theta = \frac{\sqrt{3}}{2} \implies \theta = \frac{\pi}{3} \text{ (1st quadrant)} \text{ and } \theta = \frac{2\pi}{3} \text{ (2nd quadrant)}
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