Let's do some calculus! (30)

Calculus Level 4

$\large \lim_{x \to 0} \frac{\ln \left[\cot \left( \frac \pi 4 - k_1 x \right)\right]}{\tan \left(k_2 x\right)} = 1$

If real numbers $k_1$ and $k_2$ satisfy the equation above. Find the value of $\dfrac {k_2} {k_1}$ .

Notation: $\ln (\cdot)$ denotes the natural logarithm function, that is $\log_{e}{(\cdot)}$ .