A patient receives a medical radioactive isotope. The biological half-life is $12$ hours, and the physical half-life is $6$ hours. The effective half-life $T_{eff}$ is given by $\frac{1}{T_{eff}} = \frac{1}{T_{bio}} + \frac{1}{T_{phys}}$. What is the effective half-life of the isotope in the patient's body?