Use the following approximation \[ \left(1+x^{2}\right)^{-3} \approx 1-3 x^{2}+6 x^{4}-10 x^{6}+15 x^{8}-21 x^{10} \] to estimate $\left(\frac{16}{17}\right)^{3}$. Round the answer to three decimal places.

Step 1 ：Rewrite \(\left(\frac{16}{17}\right)^{3}\) as \(\left(1-\frac{1}{17}\right)^{3}\), which is in the form of \(\left(1+x^{2}\right)^{-3}\) where \(x^2 = -\frac{1}{17}\).

Step 2 ：Substitute \(x^2\) into the approximation and calculate the result.

Step 3 ：\(x^2 = -0.058823529411764705\)

Step 4 ：approximation = 1.199461635925308

Step 5 ：Final Answer: The approximation of \(\left(\frac{16}{17}\right)^{3}\) is \(\boxed{1.199}\).