Primarily, one is not allowed to face the exact Qibla while relieving himself/herself nor turn his/her back towards Qibla as mentioned in various Ahadith due to the sanctity of the Qibla.

Nabi Sallallahu Alaihi Wasallam is reported to have said:

"When one of you arrives to defecate, then do not face the Qibla while defecating, nor while urinating. And do not have your back towards it (while defecating or urinating)." (Tirmidhi #9) 

Moreover, facing the direction of Qibla is likewise prohibited in Shariah (Shaami Vol. 1 Pg. 341) as the direction of the Qibla also stands as Qibla (up to 45 degrees) for those who are away from Baytullah/Kabah and do not see it. However, for those who can see the Baytullah/Kabah, it is incumbent upon them to face the exact Qibla in Salah; likewise, facing the exact Qibla will be prohibited while relieving. (Jawahirul Fiqh Vol. 2 Pg. 356) 

After mentioning the facts, we proceed to your query:

In the enquired scenario, it will be necessary to build the toilets 45 degrees away from the Qibla since the direction of the Qibla (up to 45 degrees) is also regarded as Qibla for those who do not perceive and sight Baytullah/Kabah. (Kitabun Nawazil Vol. 15 Pg. 305). However, for those who sight it, only the exact Qibla will be taken into consideration with regards to Salah and toilets as cited earlier.

AND ALLAH TA'AALA ALONE IN HIS INFINITE KNOWLEDGE KNOWS BEST

ANSWERED BY: MOHSIN KHAN 

Islamic Date: ١ ذو الحجة ١٤٤٠ 

English Date: 03 August 2019