Hello!

I upload my file which has a problem. I am not an expert
on MAPLE v10.05. The file name is "mapleprime-2".

I try to get a solution of four equations with the
symmetric assumption for time variables. Anyone could
change the assumption to get a result. Or, anyone could
add just two more time variables: t[6] with minus sign
amplitude and t[7] with plus sign amplitude.
So, the entire number of time variables are still
odd number which can not be changed. The current code is
following as:

restart:
eq1:=expand(sum((-1)^(i+1)*cos(w*t[i]),i=1..5)=0):
eq2:=expand(sum((-1)^(i+1)*sin(w*t[i]),i=1..5)=0):
eq3:=expand(sum((-1)^(i+1)*cos(r*w*t[i]),i=1..5)=0):
eq4:=expand(sum((-1)^(i+1)*sin(r*w*t[i]),i=1..5)=0):
t[1],t[4],t[5]:=0,2*t[3]-t[2],2*t[3]:
_EnvAllSolutions:=true:
_EnvExplicit:=true:
s1:=solve({eq1,eq2,eq3,eq4},{t[2],t[3],r});
s2:=eval(s1,[_Z93=1,_Z47=1,_Z13=1,_Z51=1,_Z107=1,_Z17=1]);
Solution_Check:=eval([eq1,eq2,eq3,eq4],s2[2]);

At the end of my maple worksheet, the solutions do not
meet the given equations: eq1, eq2, eq3 and eq4.
Could anyone explain it to me?
So, Could anyone help me to get a solution?

Thanks

The file can be found in the File Manager