I am not yet super familiar with the way beamwidth are calculated, but from what I've read, it's based on the point where the strength of the signal reaches -3dB.
Here is an excerpt from CCNA Wireless 200-355 Official Cert Guide.
I don't know if I'm reading the diagram incorrectly but it seems clear to me that the lines from which the angle is calculated are crossing the signal at around -6 ~ -7dB and definitely not -3dB.
Why is this beamwidth measured from below -5dB ? Should it be -6dB because it's twice -3dB for reasons I'm not aware of ?