Solve the equation on the interval $0 \leq \theta< 2 \pi$.
\[
\cos \left(2 \theta-\frac{\pi}{2}\right)=1
\]
What are the solutions in the interval $0 \leq \theta< 2 \pi$ ? Select the correct choice and fill in any answer boxes in your choice below.
A. The solution set is
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. There is no solution.
(C) Time Remaining: 00:58:10
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Step 1 ：First, we need to isolate the cosine function. The equation is already in the form \(\cos \left(2 \theta-\frac{\pi}{2}\right)=1\), so we don't need to do anything here.

Step 2 ：Next, we need to find the values of \(2 \theta-\frac{\pi}{2}\) that make the cosine function equal to 1. We know that \(\cos \theta = 1\) when \(\theta = 0\) or \(\theta = 2\pi\) in the interval \([0, 2\pi)\). So, we have \(2 \theta-\frac{\pi}{2} = 0\) or \(2 \theta-\frac{\pi}{2} = 2\pi\).

Step 3 ：Solving the first equation \(2 \theta-\frac{\pi}{2} = 0\) for \(\theta\), we get \(\theta = \frac{\pi}{4}\).

Step 4 ：Solving the second equation \(2 \theta-\frac{\pi}{2} = 2\pi\) for \(\theta\), we get \(\theta = \frac{5\pi}{4}\).

Step 5 ：Therefore, the solutions to the equation \(\cos \left(2 \theta-\frac{\pi}{2}\right)=1\) in the interval \([0,2 \pi)\) are \(\theta = \frac{\pi}{4}, \frac{5\pi}{4}\).

Step 6 ：Finally, we check our solutions. Substituting \(\theta = \frac{\pi}{4}\) into the original equation, we get \(\cos \left(2 \cdot \frac{\pi}{4}-\frac{\pi}{2}\right)=1\), which simplifies to \(1=1\). Substituting \(\theta = \frac{5\pi}{4}\) into the original equation, we get \(\cos \left(2 \cdot \frac{5\pi}{4}-\frac{\pi}{2}\right)=1\), which also simplifies to \(1=1\). Therefore, our solutions are correct.

Step 7 ：So, the solutions to the equation \(\cos \left(2 \theta-\frac{\pi}{2}\right)=1\) in the interval \([0,2 \pi)\) are \(\boxed{\theta = \frac{\pi}{4}, \frac{5\pi}{4}}\).