$β$	$1 + 2 \cos (ϕ + \frac{4 π}{3})$	${(\frac{2}{3})}^{\frac{1}{2}} β^{\frac{1}{2}}$	Error %	${(\frac{2}{3})}^{\frac{1}{2}} β^{\frac{1}{2}} + \frac{1}{9} β$	Error %
0	0	0	0	0	0
0.1	0.2707	0.2582	4.62	0.2693	0.52
0.2	0.3916	0.3651	6.77	0.3873	1.10
0.3	0.4888	0.4472	8.51	0.4805	1.7
0.4	0.5743	0.5164	10.08	0.5608	2.35
0.5	0.6527	0.5774	11.54	0.6329	3.03
0.6	0.7265	0.6325	12.94	0.6992	3.76
0.7	0.7972	0.6831	14.31	0.7609	4.55
0.8	0.8659	0.7303	15.66	0.8192	5.39
0.9	0.9332	0.7746	17.00	0.8746	6.28
1	1	0.8165	18.35	0.9276	7.24