Per the Manyshot Tooltip: Activating this ability reduces your Extra Shot by 100% for 70 seconds
Per the 10K Stars Tooltip: Activating this ability reduces your Extra Shot by 100% for 45 seconds
Say you are a Monkcher using the standard rotation of:
30 secs of 10K, 20 secs of MS, 10 secs of Single shot, 30 secs of 10K, 30 secs of Single, repeat from beginning
Your MS debuffs your 10 secs of Single Shot and your second 10K debuffs 15 secs of the 30 seconds of Single, leaving you with just 15 secs out of 2 minutes where Doubleshot can actually work.
For L18-20 Rangers with the T4 and T5 core, your Doubleshot is debuffed for 50 seconds of the 100 seconds where you are waiting for MS to recycle.
So is Doubleshot really worth it?
Personally I think the Devs went overboard on the Manyshot debuff. If they want to preclude Monkchers from benefitting from DS, then just extend the 10K star debuff to 60 seconds. But making MS have a 70 sec debuff only really punishes those builds who use Manyshot whose sustained ranged DPS is really not that overpowered even if loaded up with as much Doubleshot as the game provides.