As shown in the following figure, let $d_1, d_2, d_3$ denote three uncorrelated clockwise directions, observed at point $P$ with equal standard errors for each direction, i.e., $\sigma_{d_1} = \sigma_{d_2} = \sigma_{d_3} = \pm \sqrt{2}''$. Let $\alpha_1$ and $\alpha_2$ be two included angles formed by these three directions. The covariance matrix (in arcsecond$^2$) for these included angles will be given as:
Here, the covariance matrix would typically be presented in a LaTeX format, but for now we are using a placeholder.
