Let $θ$ have minimal polynomial $t^3 +at^2 +bt +c$ over $\mathbb{Q}$. In what conditions in terms of $a,b,c$ $θ =φ^2$ where $φ ∈\mathbb{Q}(θ)$

Question

This problem is Excercise 18.10 from Ian Stewart's Galois Theory. It gives a hint: Consider the minimal polynomial of $φ$. Here is my work for now:

Since $\theta=φ^2$, $φ \notin \mathbb{Q}$, and $\mathbb{Q}(\theta) = \mathbb{Q}(φ)$. So the degree of the minimal plynomial of $φ$ is 3.

$φ$ satisfies: $t^6+at^4+bt^2+c$, and it has a irreducible deg-3 polynomial as factor.

And I have no idea how to go on. So can you please give some clue?