Answer:

sin8θ−cos8θ)=(sin4θ)2−(cos4θ)2=(sin4θ−cos4θ)(sin4θ+cos4θ)

⇒LHS=(sin2θ−cos2θ)(sin2θ+cos2θ)(sin4θ+cos4θ)

⇒LHS=(sin2θ−cos2θ)[(sin2θ)2+(cos2θ)2+2sin2θcos2θ−2sin2θcos2θ]

⇒LHS=(sin2θ−cos2θ)[(sin2θ+cos2θ)2−2s