Simplify
$$\delta(t - 1) e^{i\pi t} + \delta(t - 2) e^{-i \pi t}$$
I don't understand how to simplify this. My two guesses were either there was a property with the delta function or the delta function was a red herring and I needed to use Euler's equation. I know the answer is
$$-\delta(t - 1) + \delta(t - 2)$$
but do not see how to get rid of the exponential.
$$\delta(x - a)f(x) = \delta(x-a)\ f(a)$$
Remember also that
$$e^{2\pi i} = 1$$
$$e^{\pi i} = -1$$