If A, B and C are angles of triangle, then the value of sin2⁡Acot⁡A1sin2⁡Bcot⁡B1sin2⁡Ccot⁡C1 is

Applying R2→R2−R1 and R3→R3−R1, we getΔ=sin2⁡Acot⁡A1sin⁡(B+A)sin⁡(B−A)sin⁡(A−B)sin⁡Asin⁡B0sin⁡(C+A)sin⁡(C−A)sin⁡(A−C)sin⁡Asin⁡C0             ∵cot⁡α−cot⁡β=sin⁡(β−α)sin⁡αsin⁡βExpanding along C3, we getΔ=sin⁡(A−B)sin⁡(A−C)sin⁡A−sin⁡(B+A)sin⁡C+sin⁡(C+A)sin⁡B=sin⁡(A−B)sin⁡(A−C)sin⁡A−sin⁡(π−C)sin⁡C+sin⁡(π−B)sin⁡B=sin⁡(A−B)sin⁡(A−C)sin⁡A−sin⁡Csin⁡C+sin⁡Bsin⁡B=0