Solve the equation. Give a general formula for all the solutions. List six solutions. \[ \sin \theta=\frac{\sqrt{3}}{2} \] Identify the general formula for all the solutions to $\sin \theta=\frac{\sqrt{3}}{2}$ based on the smaller angle. \[ \theta=\square, k \text { is an integer } \] an expression using $k$ as the variable.)

Step 1 ：The given equation is \(\sin \theta=\frac{\sqrt{3}}{2}\)

Step 2 ：The sine function has a value of \(\frac{\sqrt{3}}{2}\) at \(\theta = \frac{\pi}{3}\) and \(\theta = \frac{2\pi}{3}\) in the interval \([0, 2\pi)\)

Step 3 ：The general solution for the equation \(\sin \theta=\frac{\sqrt{3}}{2}\) can be written as \(\theta = \frac{\pi}{3} + 2k\pi\) and \(\theta = \frac{2\pi}{3} + 2k\pi\) where \(k\) is an integer

Step 4 ：For \(k = 0\), the solutions are \(\theta = \frac{\pi}{3}\) and \(\theta = \frac{2\pi}{3}\)

Step 5 ：For \(k = 1\), the solutions are \(\theta = \frac{\pi}{3} + 2\pi = \frac{7\pi}{3}\) and \(\theta = \frac{2\pi}{3} + 2\pi = \frac{8\pi}{3}\)

Step 6 ：For \(k = -1\), the solutions are \(\theta = \frac{\pi}{3} - 2\pi = -\frac{5\pi}{3}\) and \(\theta = \frac{2\pi}{3} - 2\pi = -\frac{4\pi}{3}\)

Step 7 ：So, the six solutions are \(\boxed{\frac{\pi}{3}}\), \(\boxed{\frac{2\pi}{3}}\), \(\boxed{\frac{7\pi}{3}}\), \(\boxed{\frac{8\pi}{3}}\), \(\boxed{-\frac{5\pi}{3}}\), and \(\boxed{-\frac{4\pi}{3}}\)