Solution

$$\sin 3=\sin \left [ \pi -\left ( \pi -3 \right ) \right ]=\sin \left ( \pi -3 \right ) \approx \sin \left ( 0.14 \right )$$

$$\sin 2=\sin \left [ \pi -\left ( \pi -2 \right ) \right ]=\sin \left ( \pi -2 \right )\approx \sin \left ( 1.14 \right )$$

$$\sin 7=\sin \left [ 2\pi +\left ( 7-2\pi \right ) \right ]=\sin \left ( 7-2\pi \right )\approx \sin \left ( 0.72 \right )$$

now $$1.14 > 1 > 0.72 > 0.14$$

$$\Rightarrow \sin \left ( 1.14 \right )> \sin 1> \sin \left ( 0.72 \right )> \sin \left ( 0.14 \right )$$[ as $$1.14, 1, 0.72,1.14$$ lie in the first quadrant and sine functions increase in the first quadrant ]

$$\sin \left ( 1.14 \right )> \sin 1> \sin \left ( 0.72 \right )> \sin \left ( 0.14 \right )$$
Hence, $$sin3$$ is least.