 Solution

Treat the repeated angles as independent measurements of one fixed angle. Their sample mean, sample standard deviation and standard error of the mean areFor $y=A\cos \theta$, uncorrelated standard uncertainties giveInterpreting the stated 1% amplitude accuracy as a standard uncertainty,Use radians in the derivative. This is uncertainty in the result using the mean angle, not the spread of individual angle measurements; the latter convention would use $s_{\theta }$ and give about $2.34\%$. An accuracy bound or systematic angular calibration error would require a different uncertainty model.