If sinθ+sin2θ=1 and acos12θ+bcos10θ+c  cos8θ+d cos6θ−1=0 then b+ca+d  =

sinθ=cos2θ ∴    asin6θ+bsin5θ+csin4θ+dsin3θ=1 →(1) and sin2θ+sinθ=1 Cubing on both sides∴    sin6θ+3sin5θ+3sin4θ+sin3θ=1 →(2) Compare, a=d=1 & b=c=3 ∴  b+ca+d=62=3