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Someone might argue against this but if drilling the screw in on an angle allows it to go all the way in and sit flush I think that'll achieve what you're after which is the required pull out resistance and shear capacity. My suggestion would be to drill on a downward angle though and also ensure that the required angle isn't too steep otherwise you'd pull the timber out.
Blackie, Did you have trouble drilling or screwing?
If it was screwing then all you need is a wider pilot whole.
If it was drilling then you need a corded drill. Wireless drills sometimes have trouble drilling into studs, specially the cheaper ones.
I had trouble drilling and yes you're right it was a cordless drill.
The shorter screw was nice and tight in the top hole but ain't as secure on the next two. Nevertheless it holds and I'm watching TV.