Step 1: Draw a figure based on the data provided.
Distance to the solar system from the star AC = 4.29 ly
Converting light years to parsec
The distance traveled by light in one year is one light year.
1 year of light = speed of light * 1 year [math] = 94608 * 10^{11} [math] m
4.29 ly = 4.29 * 94608 * 10^{11} = 405868.32*10^{11} m
4.29 ly = \frac{405868.32 *10^{11}}{3.08*10^{16}} = 1.32 \text{ persec } \because 1 \text{ parsec } = 3.08 * 10^{16} m
Diameter of the earth AB=3*10^{11} m

Step 2: Calculating the parallax angle \theta
\theta = \frac{AB}{AC}
\theta = \frac{3* 10^{11}}{405868.32* 10^{11} }
\theta = 7.39 * 10^{-6}
Hence, parallax angle \theta = 7.39 * 10^{-6} rad = 1.5 seconds