Question: solve trigonometric equations

Dear Sir/Madam:

I have the following simultaneous equations to get the 4 unknow variables
by maple engine. However, the maple did not give me anything. Actually,
the exact solutions exist in the educational text. Now, I am trying to get them
on maple. Why it does not work at all?
Please let me know how to do.

Thanks in advance.

restart;
eq1:=A2*t2*exp(zt*t2*om)*sin(t2*wd)+A3*t3*sin(t3*wd)*exp(zt*t3*om) = 0:
eq2:=A2*t2*exp(zt*t2*om)*cos(t2*wd)+A3*t3*cos(t3*wd)*exp(zt*t3*om) = 0:
eq3:=              A2*exp(zt*t2*om)*sin(t2*wd)+A3*sin(t3*wd)*exp(zt*t3*om) = 0:
eq4:=1-A2-A3+A2*exp(zt*t2*om)*cos(t2*wd)+A3*cos(t3*wd)*exp(zt*t3*om) = 0:
_EnvAllSolution := true:
_EnvExplicit := true:
s1:=solve({eq1,eq2,eq3,eq4},{t2,t3,A2,A3}) assuming A2>0,A3>0,t2>0,t3>0,zt>=0,zt<1,wd>0,om>0;