How to deal with error caused by sign change in arcsin?

Question

The problem happens in antenna array signal processing.
I have two antennas A and B. According to the complex signal received, I have the phases pA and pB. Both pA and pB are between -$\pi$ and $\pi$. So dp = pA-pB falls between -2$\pi$ and 2$\pi$. The final result is calculated by AOA = arcsin(dp/$\pi$), so I need to wrap dp to -$\pi$ and $\pi$ first. Then the issue comes.
Suppose the ground truth of dp is $\pi$-0.01. And I have multiple noisy observations of dp. Take two observations dp1 and dp2 for example. dp1=$-\pi$-0.02, and dp2=$\pi$+0.01. After wrapping, dp2 becomes $-\pi$+0.01. So AOA1 = arcsin(dp1/$\pi$) is around $\pi/2$, AOA2 = arcsin(dp2/$\pi$) is around $-\pi/2$. So dp1-dp2=-0.02, and AOA1-AOA2=$-\pi$. A small change in dp causes huge change in AOA.
If dp1 is $\pi$-0.02 and dp2 is $\pi$-0.04, then AOA1-AOA2 is 0.0468.
In this case, if I make multiple noisy observations around dp=$\pi$, almost half of the AOA difference will have a large absolute value like -$\pi$, and the other half will have a small absolution value like 0.0468. This is definitely what I want for further analysis.
What can be done to avoid this situation? Thanks!