Potassium dichromate \( (K_2Cr_2O_7) \) is prepared from chromite ore \( (FeCr_2O_4) \) through the following
steps: 1. Roasting with Sodium Carbonate: \[ FeCr_2O_4 + 4Na_2CO_3 + 7O_2 \rightarrow 2Na_2CrO_4 + 2Fe_2O_3 + 4CO_2 \]
2. Conversion to Dichromate: \[ 2Na_2CrO_4 + H_2SO_4 \rightarrow Na_2Cr_2O_7 + Na_2SO_4 + H_2O \]
3. Formation of Potassium Dichromate: \[ Na_2Cr_2O_7 + 2KCl \rightarrow K_2Cr_2O_7 + 2NaCl \]
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 ___________.