Absolute angular rotation rate measurements with sensitivity better than prad/s would be beneficial for fundamental science investigations. In this regard, large frame Earth based ring laser gyroscopes are top instrumentation as far as bandwidth, long-term operation, and sensitivity are concerned. Here, we demonstrate that the GINGERINO active-ring laser upper limiting noise is close to 2×10^{-15} rad/s for ∼2×10^{5} s of integration time, as estimated by the Allan deviation evaluated in a differential measurement scheme. This result is more than a factor of 10 better than the theoretical prediction so far accounted for ideal ring lasers shot-noise with the two beams counterpropagating inside the cavity considered as two independent propagating modes. This feature is related to the peculiarity of real ring laser system dynamics that causes phase crosstalking among the two counterpropagating modes. In this context, the independent beam model is, then, not applicable, and the measured noise limit falls below the expected one.