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I am trying to solve this equation in sage $$\sqrt{-4 \, z^{2} + 2 \, \sqrt{-4 \, z^{2} + 1} - 1} = 0.$$ But when I try the code

var('z')
eq = sqrt(-4*z^2 + 2*sqrt(-4*z^2 + 1) - 1) == 0
solve(eq,z)

I get

[z == -1/2*sqrt(2*sqrt(-4*z^2 + 1) - 1), z == 1/2*sqrt(2*sqrt(-4*z^2 + 1) - 1)]

Is there any way to actually solve it in sage?