OK, i found the same issue with my front camera, so when i wanted to face time my Grand children i found my screen was black, rear camera worked fine, but front camera had nothing, i knew it worked only last week, so i went into settings, then privacy, down to camera, and i unchecked all to boxes, so there was nothing in green, went back to my front facing camera, and camera is working again, so tells me that one on the apps allowed to used the camera is causing an issue, its now elliminating which one by switching then all back on one by one, so turn one on and check the camera, if ok then go back and switch on another, and so on until you found the app causing the issue, good luck, BTW this is on my Iphone 5s, ios 10.3.2.