Lie group representation and inner product

Question

Let $G$ be a connected semisimple Lie group.Now let $\theta$ be the Cartan involution of $G$ and let $(\pi,V)$ be a finite dimensional representation of $G$. On page 22 of Analysis and geometry on complex homogeneous domains (Faraut et al), they state that there exists an inner product on $V$ such that $$\pi(g)^* = \pi(\theta(g)^{-1}).$$ Why is this the case?