TeX source:

\langle\psi|\rho^\top|\psi\rangle = \text{tr}(\langle\psi|\rho^\top|\psi\rangle) = \text{tr}\{(\langle\psi|\rho^\top|\psi\rangle)^\top\} = \text{tr}(\langle\psi|\rho|\psi\rangle) = \langle\psi|\rho|\psi\rangle.