please help me to solve nonlinear equations

.5<m<1

[(3*(Cos[x1] - Cos[x2] + Cos[x6] - Cos[x7])+4*(Cos[x3] - Cos[x4] + Cos[x5])-7*Pi*(m)/4)=0,
(3*(Cos[5 x1] - Cos[5 x2] + Cos[5 x6] - Cos[5 x7])+4*(Cos[5 x3] - Cos[5 x4] + Cos[5 x5]))=0,
(3*(Cos[7 x1] - Cos[7 x2] + Cos[7 x6] - Cos[7 x7]) + 4*(Cos[7 x3] - Cos[7 x4] + Cos[7 x5]))=0,
(3*(Cos[11 x1] - Cos[11 x2] + Cos[11 x6] - Cos[11 x7])+4*(Cos[11 x3] - Cos[11 x4] + Cos[11 x5]))=0,
(3*(Cos[13 x1] - Cos[13 x2] + Cos[13 x6] - Cos[13 x7])+4*(Cos[13 x3] - Cos[13 x4] + Cos[13 x5]))=0,
(3*(Cos[17 x1] - Cos[17 x2] + Cos[17 x6] - Cos[17 x7])+4*(Cos[17 x3] - Cos[17 x4] + Cos[17 x5]))=0,
(1.3*(Cos[x1] - Cos[x2] + Cos[x6] - Cos[x7]) - (Cos[x3] - Cos[x4] + Cos[x5]))=0  
{0.05 < x1 < x2 < x3 < x4 < x5 < x6 < x7 < Pi/2 }

[Walter Roberson]

Someone else has posted a number of these kinds of questions over the last while. A persistent question that has not been answered is whether it is desired to find one solution or if it is required to find all solutions ?

[Walter Roberson]

Analytically you cannot really reduce this by more than 2 variables, in that any additional reductions become too unwieldly. The second reduction results at best in a root of a 5th order equation for the second variable, with the alternatives being worse.