We study the polymerization kinetics and linear rheology of actin filaments in the absence and in the presence of latrunculin A. Filamentous actin is a semiflexible polymer, and latrunculin A is an organic, actin-binding molecule. Using diffusing wave spectroscopy (DWS), we monitor the thermally excited motion of monodisperse polystyrene microspheres in semidilute solutions of actin filaments. From these measurements, we extract the microspheres mean-square displacement, which is related to the viscoelastic nature of the actin solutions. These optical measurements, along with mechanical measurements, suggest that despite its depolymerizing effect, latrunculin A promotes the strengthening of actin networks. DWS shows that while the scaling nature of the viscoelastic properties of actin filaments is essentially unmodified in the presence of latrunculin A at small time scales, the elasticity of actin solutions becomes enhanced for increasing latrunculin concentrations at large time scales. Complementary electron-microscopy measurements help uncover the structural origin of this enhanced elasticity at small time scales.