$3\tau(K_1$#$K_2)$=$\tau(K_1)\tau(K_2)$

Question

Suppose we have two knots $K_1$ and $K_2$. Then look to the connected sum of $K_1$ and $K_2$ denoted by $K_1\#K_2$ (defined for knots). Suppose $\tau$ is the number of $3$-colourings (definition for knots). I want to prove the formula above, namely: $3\tau(K_1\#K_2)=\tau(K_1)\tau(K_2)$. I read about some proofs with help of $n$-tangles. But i ask myself if there are proofs without such tangles?? Is it possible to come to the solution just with counting??