Write a computer program in the language/environment of your choice to solve the \(\theta-\beta-M\) relation [Equation (9.23)] for \(\beta\) given \(\theta\) and \(M\).

9.23:

\(\tan \theta=2 \cot \beta \frac{M_1^2 \sin ^2 \beta-1}{M_1^2(\gamma+\cos 2 \beta)+2}\)

Check your results against the \(\theta-\beta-M\) plot. Hints: Write a function whose value equals zero at the proper value of \(\beta\). Then, use Newton's method to find the zeros of the function. Choosing \(\beta=1\) as your initial guess will result in convergence to the weak solution, whereas choosing \(\beta=89\) will result in convergence to the strong solution. MATLAB and MS Excel's Visual Basic environment are good platforms for doing this because their other features make it easy to use your function's output to solve problems.