If $$sin θ + sin^2θ + sin^3θ = 1$$, then $$cos^6θ - 4cos^4θ + 8cos^2θ$$ is equal to

Expression : $$sin θ + sin^2θ + sin^3θ = 1$$

=> $$sin \theta + sin^3 \theta = 1 - sin^2 \theta$$

=> $$sin \theta (1 + sin^2 \theta) = cos^2 \theta$$

Squaring both sides

=> $$(sin^2 \theta) (1 + sin^2 \theta)^2 = cos^4 \theta$$

=> $$(1 - cos^2 \theta) (1 + 1 - cos^2 \theta)^2 = cos^4 \theta$$

=> $$(1 - cos^2 \theta) (4 - 4cos^2 \theta + cos^4 \theta) = cos^4 \theta$$

=> $$4 - 4cos^2 \theta + cos^4 \theta - 4cos^2 \theta + 4cos^4 \theta - cos^6 \theta = cos^4 \theta$$

=> $$- cos^6 \theta + 4cos^4 \theta - 8cos^2 \theta + 4 = 0$$

=> $$cos^6 \theta - 4cos^4 \theta + 8cos^2 \theta = 4$$