The value of $$\frac{4}{1+tan^2 θ} + \frac{1}{1+cot^2 θ} + 3 sin^2 θ$$

Expression : $$\frac{1}{1+cot^2 θ} + \frac{4}{1+tan^2 θ} + 3 sin^2 θ $$

= $$\frac{1}{1 + \frac{cos^2 \theta}{sin^2 \theta}} + \frac{4}{1 + \frac{sin^2 \theta}{cos^2 \theta}} + 3 sin^2 \theta$$

= $$\frac{sin^2 \theta}{cos^2 \theta + sin^2 \theta} + \frac{4 cos^2 \theta}{cos^2 \theta + sin^2 \theta} + 3 sin^2 \theta$$

= $$sin^2 \theta + 4 cos^2 \theta + 3 sin^2 \theta$$

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