En el siguiente diagrama, $O$ es el centro del círculo. Si tres ángulos $\alpha, \beta$ y $\gamma$ son iguales, encuentra $\alpha.$ [asy]\nunitsize(40);\nimport graph; size(300); real lsf = 0.5; pen dp = linewidth(0.7) + fontsize(10); defaultpen(dp); pen ds = black; pen ttttff = rgb(0.2,0.2,1); pen ffttww = rgb(1,0.2,0.4); pen qqwuqq = rgb(0,0.39,0);\ndraw(circle((0,0),2.33),ttttff+linewidth(2.8pt)); draw((-1.95,-1.27)--(0.64,2.24),ffttww+linewidth(2pt)); draw((0.64,2.24)--(1.67,-1.63),ffttww+linewidth(2pt)); draw((-1.95,-1.27)--(1.06,0.67),ffttww+linewidth(2pt)); draw((1.67,-1.63)--(-0.6,0.56),ffttww+linewidth(2pt)); draw((-0.6,0.56)--(1.06,0.67),ffttww+linewidth(2pt)); pair parametricplot0_cus(real t){\nreturn (0.6*cos(t)+0.64,0.6*sin(t)+2.24);\n}\ndraw(graph(parametricplot0_cus,-2.2073069497794027,-1.3111498158746024)--(0.64,2.24)--cycle,qqwuqq); pair parametricplot1_cus(real t){\nreturn (0.6*cos(t)+-0.6,0.6*sin(t)+0.56);\n}\ndraw(graph(parametricplot1_cus,0.06654165390165974,0.9342857038103908)--(-0.6,0.56)--cycle,qqwuqq); pair parametricplot2_cus(real t){\nreturn (0.6*cos(t)+-0.6,0.6*sin(t)+0.56);\n}\ndraw(graph(parametricplot2_cus,-0.766242589858673,0.06654165390165967)--(-0.6,0.56)--cycle,qqwuqq);\ndot((0,0),ds); label('$O$', (-0.2,-0.38), NE*lsf); dot((0.64,2.24),ds); label('$A$', (0.72,2.36), NE*lsf); dot((-1.95,-1.27),ds); label('$B$', (-2.2,-1.58), NE*lsf); dot((1.67,-1.63),ds); label('$C$', (1.78,-1.96), NE*lsf); dot((1.06,0.67),ds); label('$E$', (1.14,0.78), NE*lsf); dot((-0.6,0.56),ds); label('$D$', (-0.92,0.7), NE*lsf); label('$\alpha$', (0.48,1.38),NE*lsf); label('$\beta$', (-0.02,0.94),NE*lsf); label('$\gamma$', (0.04,0.22),NE*lsf); clip((-8.84,-9.24)--(-8.84,8)--(11.64,8)--(11.64,-9.24)--cycle);\n[/asy]