Acetaldehyde \( (CH_3CHO) \) can be converted to isopropyl alcohol \( (CH_3CH(OH)CH_3) \) through the following steps:
1. Aldol Condensation: \[ 2CH_3CHO \xrightarrow{\text{Dil. NaOH}} CH_3CH(OH)CH_2CHO \]
2. Catalytic Hydrogenation: \[ CH_3CH(OH)CH_2CHO + H_2 \xrightarrow{\text{Ni, Heat}} CH_3CH(OH)CH_3 \] Thus, acetaldehyde undergoes aldol condensation followed by hydrogenation to yield isopropyl alcohol.
Explain the construction of a spherical wavefront by using Huygens' principle.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.