I'm not sure how to approach this problem. the only idea i can think of is the cross product but i didn't see an example of that in the book for this type of problem so I'm not sure. I can't find similar solutions online either. If anyone can tell me how to approach this problem that'd be amazing. thanks.
See $ \bf{r_1}$ is position vectors of curve. So here, $\Delta \bf{r}$ = $\bf r_f- r_i$ represents a secant, and the limit as $ \Delta \bf{r}$ tends to zero, ie $ d\bf{r}$ represents a tangent.
Thus tangents to these vectors can also be represented by $\dfrac{d\bf{r}}{dt}$. So you can find the value of $\cos(\theta)$ at $t = 0$:
$$\cos(\theta_0) = \dfrac{\bf{\dot{r_1}} \cdot \bf{\dot{r_2}}}{|\bf{\dot{r_1}}||\bf{\dot{r_2}}|} \rvert_{t=0}$$
where $ \bf{\dot{r}} =$ $\dfrac{d\bf{r}}{dt}$