Step 1 :Define the given equation as \(2\sin(t)^2 - \sin(t) - 1 = 0\).
Step 2 :Solve the equation for \(t\). The solutions are \(-\pi/6\), \(\pi/2\), and \(7\pi/6\).
Step 3 :However, the question asks for the solutions in the interval \([0, 2\pi]\). The solution \(-\pi/6\) is not in this interval.
Step 4 :Add \(2\pi\) to the solution \(-\pi/6\) to get a solution in the interval \([0, 2\pi]\). The solution \(-\pi/6 + 2\pi\) is equal to \(11\pi/6\).
Step 5 :Therefore, the solutions for \(t\) in the interval \([0, 2\pi]\) are \(\pi/2\), \(7\pi/6\), and \(11\pi/6\).
Step 6 :Final Answer: \(\boxed{\frac{\pi}{2}, \frac{7\pi}{6}, \frac{11\pi}{6}}\)