System of Equations

Could anyone please teach me how to solve the following system of equations?

-x^2-(y-1)^2+1<=0
2(1-z)x=0
-2z(y-1)-cos(y)=0
z(-x^2-(y-1)^2+1)=0
z>=0
-2<=y<=2 (radian)
x,z are real numbers

It seems that there are a lot of possible solutions before using the inequality to do the rejection, how can we avoid missing any possible solutions?
Please give me some explanations if it is possible.
Thanks!