c++ - Changing coordinate system causes clockwise rotations

The task I need to convert the coordinate system to +X forward, +Y right and +Z up (left-handed, like the one in Unreal Engine). The crucial part is that I want my camera to face its forward axis (

c++ - Changing coordinate system causes clockwise rotations

c++ - Changing coordinate system causes clockwise rotations

c++ - Changing coordinate system causes clockwise rotations

c++ - Changing coordinate system causes clockwise rotations