In a `!ABC` , there is a point `D` on the side BC such that `(BD)/(DC)` =`1/3`.If `angleB=pi/3,angleC=pi/4` and `sinangle(CAD)=lamdasinangleBAD` then `lamda` is equal to

Options

A. `1/(sqrt6)`
B. `sqrt6`
C. `1/(sqrt3)`
D. `sqrt3`

Explanation

To solve the problem step by step, we will use the properties of triangles and the sine rule.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Triangle \( ABC \) with point \( D \) on side \( BC \).
- The ratio \( \frac{BD}{DC} = \frac{1}{3} \).
- Angles: \( \angle B = \frac{\pi}{3} \) and \( \angle C = \frac{\pi}{4} \).
...