If sin⁡x+sin⁡y+sin⁡z+sin⁡w=−4 then the value of sin400⁡x+sin300⁡y+sin200⁡z+sin100⁡w is

sin⁡x+sin⁡y+sin⁡z+sin⁡w=−4⇒ sin⁡x=sin⁡y=sin⁡z=sin⁡w=−1 (only)   So, sin400⁡x+sin300⁡y+sin200⁡x+sin100⁡w=(−1)400+(−1)300+(−1)200+(−1)100=4