what are the 2 angles between 0 degrees and 360 degrees of the cosine value 0.6

Look here:

http://tube.geogebra.org/b/1120471#material/8029

The angles are:

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.6}}\right)} = {\mathtt{53.130\: \!102\: \!354\: \!156^{\circ}}}$$

and   $${\mathtt{360}}{\mathtt{\,-\,}}{\mathtt{53.13}} = {\mathtt{306.87}}$$      [ ° ]

Gruß radix !