### How to solve this equation with double square root?

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?