How do I correctly calculate the correlated (nondiagonal) covariance matrix?
Also, I thought of a situation where this approach will fail. Let's say $\theta_2=179$~deg and I have two measurements of $z_{12}$. After performing simplification through linear manipulation, it's possible that I'll have one measurement of $\theta_2$ that is (for example) 178 degrees, and another that is (for example) -178 degrees. When calculating $\theta_2$ by taking the weighted mean of these two measurements, I'll (incorrectly) get 0 degrees.
Also, I thought of a situation where this approach will fail. Let's say $\theta_2=179$~deg and I have two measurements of $z_{12}$. After performing simplification through linear manipulation, it's possible that I'll have one measurement of $\theta_2$ that is (for example) 178 degrees, and another that is (for example) -178 degrees. When calculating $\theta_2$ by taking the weighted mean of these two measurements, I'll (incorrectly) get 0 degrees.