Solve $8 \sin ^{2}(w)-2 \sin (w)-3=0$ for all solutions $0 \leq w<2 \pi$. \[ w= \] Give your answers as values accurate to at least two decimal places in a list separated by commas. Question Help: $\square$ Video Submit Question Jump to Answer

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 \(0 \leq w < 2\pi\). Therefore, the only solution to the equation is \(w = 0.85\).

Step 6 ：Final Answer: \(\boxed{0.85}\)