The truth is, the more haste you add, the more each additional piece of haste is even more valuable. (See Below)
First, you can have both.... Just because you use haste in your body slot doesnt' mean you can't use Brutal earring. They way you present your information is a false dichotomy; it's not either/or. You're sacrificing 4% haste for 2% Double attack. Period.
As stated above, the more haste you add, the more value haste has. Where Double Attack suffers form diminishing returns.
Best illustrated in extremes:
100 hits:
25% DA = 125 hits.
25% Haste = 133 Hits.
50% DA = 150 hits.
50% Haste = 200 hits.
75% DA = 175 hits.
75% Haste = 400 Hits.
80% DA = 180 hits.
80% Haste = 500 hits.
It's not intuitive, but haste is a reduction in the time between actions, not an increase in the amount of actions.
At 50% haste, you're removing 1/2 the delay, meaning, you're able to do 2 actions in the same time.
At 80% delay reduction(capped, reference for below), you've reduced the time between actions to a mere 20% of the original, meaning you can do 5x as much in the same time.
And you can see, the difference between 75% delay reduction and 80% is a 100% increase in hit rate. That's only 5% haste. Rapparee COULD be that 5%.
No.
The only accurate advice in your entire post.