Question: Fsolve doesn't provide the answer for highly non-linear system of equations

Hello everyone

I try to solve the system of nonlinear equations, where three variables are inside of integrals, for different values of the real parameter q.

It seems that  not for all values of q the system has a solution because I substitute different q but the function fsolve does not give any numerical answer or the special message even after the long evaluation. 

Here the code:

restart;
q := 70;
k0 := 100; n := 3; r := 1.1; t := 0.1e-2; Eg := n/((n+1)^(3/2)+1)^(2/3); kF2 := (1/((n+1)^(3/2)+1))^(1/3);
R1 := int(a^2*tanh(sqrt((a^2-mu)^2+d1^2)/(2*t))/sqrt((a^2-mu)^2+d1^2), a = 0 .. k0);
R2 := int(a^2*tanh(sqrt((a^2-mu+Eg)^2+d2^2)/(2*t))/sqrt((a^2-mu+Eg)^2+d2^2), a = 0 .. k0);
R3 := int(a^2*(1-(a^2-mu)*tanh(sqrt((a^2-mu)^2+d1^2)/(2*t))/sqrt((a^2-mu)^2+d1^2)), a = 0 .. k0);
R4 := int(a^2*(1-(a^2-mu+Eg)*tanh(sqrt((a^2-mu+Eg)^2+d2^2)/(2*t))/sqrt((a^2-mu+Eg)^2+d2^2)), a = 0 .. k0);
Eq1 := evalf(k0+k0*(r-1)-(1/2)*Pi*r*kF2*q-R1);           
Eq2 := evalf(k0-(1/2)*Pi*kF2*q-R2);
Eq3 := evalf(2/3-R3-R4);
fsolve({Eq1, Eq2, Eq3}, {d1, d2, mu});

I know that this system has the solution for some values of q but why I can't get the solution or the answer using fsolve?

Thank you in advance.

Update. I apologize, I made some errors in expressions R2 and R4. I have corrected the question and the code. But the problem is still unresolved.