- Estuve leyendo mientras esperaba.
- ¿Qué haremos mientras / entre tanto?
- Por ahora no sé nada.
Jane, Rusty, this question is not easy.
Mientras and
entre tanto / entretanto mean the same, but they are used differently. It's again, a question of placement. It's common to use
mientras in the middle or at the end of a sentence, but I don't think it is common to use
entre tanto in the middle of a sentence:
- Estaré aquí mientras.

- Estaré aquí mientras llegas.

- Estaré aquí entre tanto.

- Estaré aquí entre tanto llegas.
(it's OK, but it sounds a little odd).
Anyway, I would like to check this with other native Spanish speakers, as this can only be my way of talking.