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Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including all answers in $[0, 2 π)$ and indicating the remaining answers by using $n$ to represent any integer. Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution."
$2 \sin^{2} (x) + 2 = 4$

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Final Answer: The solutions to the equation are $x = \frac{π}{2}, \frac{3 π}{2}$ .

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Step 1 ：The given equation is a trigonometric equation. To solve it, we need to isolate the trigonometric function and then find the possible values of x. The given equation is $2 \sin^{2} (x) + 2 = 4$ .

Step 2 ：We can start by subtracting 2 from both sides to isolate the trigonometric term. This gives us $2 \sin^{2} (x) = 2$ .

Step 3 ：Then, we can divide both sides by 2 to get $\sin^{2} (x) = 1$ .

Step 4 ：Taking the square root of both sides, we get $\sin (x) = \pm 1$ .

Step 5 ：We know that sin(x) equals 1 at $\frac{π}{2}$ and -1 at $\frac{3 π}{2}$ in the interval $[0, 2 π)$ .

Step 6 ：Therefore, the solutions to the equation are $x = \frac{π}{2}, \frac{3 π}{2}$ .

Step 7 ：Final Answer: The solutions to the equation are $x = \frac{π}{2}, \frac{3 π}{2}$ .

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