Solution of cubic equation is not smooth

I am trying to find the solution of cubic equation as a function of $ kz$

-1.05976 + \[Lambda] (-4.3872 + (-3.9 -         1. \[Lambda]) \[Lambda]) + (1.10144 + 0.624 \[Lambda]) Cos[    1.31 kz] + 0.035152 Cos[2.62 kz]==0 
{e1[kz_], e2[kz_],    e3[kz_]} = \[Lambda] /.     NSolve[-1.05976 + \[Lambda] (-4.3872 + (-3.9 -         1. \[Lambda]) \[Lambda]) + (1.10144 + 0.624 \[Lambda]) Cos[    1.31 kz] + 0.035152 Cos[2.62 kz]==0, \[Lambda]] // FullSimplify 

If I plot e1[kz] as function of kz,

Plot[e1[z], {z, 0, \[Pi]/3}] 

enter image description here

I get a function that is not smooth. However, if I plot another solution alongside then it seems two solution got mixed up.

Plot[{e1[z], e3[z]}, {z, 0, \[Pi]/3}] 

enter image description here

Does anyone know why is this the case? Also, can you fix this?