Let the amount of water initially poured into the container be $x$ litres. Therefore, the amount of milk in the container is $300 - x$ litres, as the total volume is 300 litres.
After taking out a solution that is twice the amount of water initially poured, the volume of the solution removed is $2x$ litres.
Since the solution is homogeneous, the fraction of water in the removed solution is $\frac{x}{300}$ and the fraction of milk removed is $\frac{300-x}{300}$.
Water removed: $\frac{x}{300} \times 2x = \frac{2x^2}{300}$.
Milk removed: $\frac{300-x}{300} \times 2x = \frac{2x(300-x)}{300}$.
After the solution is removed, water is poured in to refill the container, so the total amount of water in the container becomes:
\[ x - \frac{2x^2}{300} + x = 2x - \frac{2x^2}{300} \]
The total amount of milk left in the container is:
\[ 300 - x - \frac{2x(300-x)}{300} \]
After refilling the container, the total volume of the solution remains 300 litres, and the resulting solution contains 72\% milk.
\[ 0.72 \times 300 = 216 \text{ litres of milk} \]
Equating the amount of milk left in the container to 216:
\[ 300 - x - \frac{2x(300-x)}{300} = 216 \]
Solving this equation for $x$, we get:
\[ x = 30 \]
Thus, the amount of water initially poured into the container is {30} litres.