Conjugacy and the Class Equation · Medium problem

In $S_7$, let $\tau = (1\,2)(3\,4\,5)(6\,7)$ and $\rho=(2\,3)(4\,5\,6)(1\,7)$ — both cycle type $(2,3,2)$. Matching corresponding cycles in the order written gives $\sigma$ with $\sigma\tau\sigma^{-1}=\rho$. What is $\sigma(1) + \sigma(3)$?