It's kinda hard to kill spiders unless you (or your bug guy) can spray them directly. You have a bunch of spiders simply because there is an ample food source for them. Kill their food, and they will go somewhere else. Killing the mosquitos and gnats is easier said than done. However, with the treat of Zika and West Nile, I've been fogging the yard 2x per day for the last few months. We are getting far fewer mosquito bites, and I'm seeing a lot few arachnids creeping around the pool and in the house lately.
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On a related note....when they started building the house next door several months ago, we got inundated by spiders. A few of the wolf spiders were the size of my hand. I didn't know we had tarantulas here in Texas!