About Jacobi Method for computing eigenvalues of matrices ( Trefethen and Bau Numerical Linear Algebra Lecture 30 Question 30.1

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Here, the problem is to derive the following formula for Jacobi Method for computing the eigenvalues of a matrix A, by diagonalizing sub-matrix of A in which the real $2$$\times$$2$ symmetric matrix can be diagonalized in the form

$J^T$$\begin{pmatrix}a&d\\d&b\end{pmatrix}$ $J$ = $\begin{pmatrix}\ne0&0\\0&\neq0\end{pmatrix}$,

where $J$ is orthognal.

What would be the precise geometric interpretation of the transformation; $tan$$2\theta$= $\frac{2d}{b-a}$ based on the choice of $\theta$ ?