Suppose that $\theta$ is a differentiable function of the variable $n$ given by the formula \[ \theta(n)=\tan ^{-1}(0.07 / n) \] Find a formula for the derivative $\theta^{\prime}(n)=\frac{d \theta}{d n}$ and use it to compute the derivative at $n=0.07$. That is, compute $\theta^{\prime}(0.07)$. Enter your answer as a decimal. Round to three decimal places (as needed).

Step 1 ：Let's consider the function \(\theta(n)=\tan ^{-1}(0.07 / n)\) where \(\theta\) is a differentiable function of the variable \(n\).

Step 2 ：We are asked to find a formula for the derivative \(\theta^{\prime}(n)=\frac{d \theta}{d n}\) and use it to compute the derivative at \(n=0.07\).

Step 3 ：First, we compute the derivative of the function. The derivative of \(\theta(n)\) with respect to \(n\) is \(\theta^{\prime}(n) = -0.07/(n^2*(1 + 0.0049/n^2))\).

Step 4 ：Next, we substitute \(n=0.07\) into the derivative function to compute the derivative at \(n=0.07\).

Step 5 ：After substituting, we find that \(\theta^{\prime}(0.07) = -7.14285714285714\).

Step 6 ：Rounding to three decimal places, we get \(\theta^{\prime}(0.07) \approx -7.143\).

Step 7 ：So, the derivative of the function \(\theta(n)=\tan ^{-1}(0.07 / n)\) at \(n=0.07\) is approximately \(\boxed{-7.143}\).