The numerical value of $$\frac{1}{1+cot^2 θ} + \frac{3}{1+tan^2 θ} + 2sin^2 θ $$ is

Expression : $$\frac{1}{1+cot^2 θ} + \frac{3}{1+tan^2 θ} + 2sin^2 θ $$

= $$\frac{1}{1 + \frac{cos^2 \theta}{sin^2 \theta}} + \frac{3}{1 + \frac{sin^2 \theta}{cos^2 \theta}} + 2 sin^2 \theta$$

= $$\frac{sin^2 \theta}{cos^2 \theta + sin^2 \theta} + \frac{3 cos^2 \theta}{cos^2 \theta + sin^2 \theta} + 2 sin^2 \theta$$

= $$sin^2 \theta + 3 cos^2 \theta + 2 sin^2 \theta$$

= $$3 (cos^2 \theta + sin^2 \theta) = 3$$