Use only cos rule to prove this $\displaystyle cotA:cotB:cotC$=$\displaystyle (b^2+c^2-a^2)$:$\displaystyle (a^2+c^2-b^2)$:$\displaystyle (a^2+b^2-c^2)$

In this case i use cos rule but, after few step i cannot simplify, but i have finish this sum with sine rule, If anyone have a idea to do simplify this sum through cos rule>>>>>>