In this context, 怎么也 means 'no matter how ...still.. ' 怎么也睡不着觉. --> He still can not fall asleep no matter how (hard he tries). Because all the thoughts he has in his mind. Hope this helps.

I guess it's a sentence from the book Harry Potter. And the original English version of the sentence is "The Dursleys got into bed. Mrs. Dursley fell asleep quickly but Mr. Dursley lay awake, turning it all over in his mind ”怎么也“ is often used to emphasize something following. e.g. 怎么也找不到 mean "can't find it at all", and "怎么也醒不来” means can't wake up at all. Hope this helps a bit.

simply,怎么也，just is a said degree of words.and it suggests he could not sleep well owning to something

he chould not sleep either (little doubt why he couldn't sleep ) but you have mistake on this sentence , if we use "怎么也“ ， that's to say he is not the only one who can;t do something ,just like , i can't sleep at night , my wife also can't sleep either , maybe i am thinking something in deep so that i can't sleep , at the moment ,i doubt why my wife could not sleep .totally mean "not ....too" implying doubt

Anyway No matter how