Question: solution to set of nonlinear equations (transcendental) equaqtions with one free parameter


I have a set of nonlinear equations (transcendental) containing variables and one free parameter. I want to solve this system for variables while varying parameter's value. I have tried with fsolve and solve commands keeping fixed the parameter value, but they are not solving yet. Is there any way to solve this system for a range of parameter's value.
The systmem is like this, x,y,z are the variables and 'a' is the parameter:

Many thanks in advance.

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