Solve $8{\sin }^2(w)-2\sin (w)-3=0$ for all solutions $0\le w<2\pi$.
$$w=$$
Give your answers as values accurate to at least two decimal places in a list separated by commas.
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Step 1 ：The given equation is a quadratic equation in terms of $\sin (w)$. We can solve it by using the quadratic formula $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, where a, b, and c are the coefficients of the quadratic equation.

Step 2 ：Let's identify the coefficients: a = 8, b = -2, c = -3.

Step 3 ：Using the quadratic formula, we find the roots of the quadratic equation to be 0.75 and -0.5.

Step 4 ：After finding the roots of the quadratic equation, we can find the values of w by taking the inverse sine of the roots.

Step 5 ：However, the inverse sine of -0.5 is not in the range $0\le w<2\pi$. Therefore, the only solution to the equation is $w=0.85$.

Step 6 ：Final Answer: $\boxed{{\displaystyle 0.85}}$