For the error estimate, you should have calculated the r.m.s. error either from the Parseval formula (probably easiest) or directly:

In[39]:=
RMSError = Sqrt[Integrate[(%% - CS[x])^2, {x,0,1}] ]
Out[39]=
                    2     4
     -3 (120 + 10 Pi  + Pi )
Sqrt[----------------------- + 
                  6
              4 Pi
 
                       3         5        7
   -65880 Pi + 10590 Pi  - 544 Pi  + 32 Pi
   ----------------------------------------]
                         7
                    64 Pi
In[40]:=
N[%]
Out[40]=
0.14196