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Consider the given equation:

$\sin(\theta) = \frac{\sqrt{2}}{2}$

We know that $\sin(\theta) = \frac{\sqrt{2}}{2}$ at $\theta = \frac{\pi}{4} + 2n\pi$ and $\theta = \frac{3\pi}{4} + 2n\pi$ for any integer $n$.

To find the solutions in the interval $[0, 2\pi)$, we consider:

$\theta = \frac{\pi}{4}$

$\theta = \frac{3\pi}{4}$

Thus, the solutions are:

$\theta = \frac{\pi}{4}, \frac{3\pi}{4}$

We start with the equation:

$sin( heta) = frac{sqrt{2}}{2}$

The sine function attains the value $frac{sqrt{2}}{2}$ at the angles:

$ heta = frac{pi}{4}$ and $ heta = frac{3pi}{4}$

To find the values in the interval $[0, 2pi)$, we look at:

$ heta = frac{pi}{4}$

$ heta = frac{3pi}{4}$

Therefore, the values of $ heta$ are:

$ heta = frac{pi}{4}, frac{3pi}{4}$

Solve:

$sin( heta) = frac{sqrt{2}}{2}$

The solutions in $[0, 2pi)$ are:

$ heta = frac{pi}{4}$ and $ heta = frac{3pi}{4}$

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