Fourier transformation of a distribution.

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I've been studying for the complex analysis exam that is to come in 4 days and i wanted some help with one of the exercises! I've been studying the solved exercises that the professor has uploaded in his uni portal but i didn't get how he did the last step! Here's the exercise:

Compute the Fourier transform of :$δ(2t) + \sin(3t)$

Here is what he did:

$F(δ(2t) + \sin(3t))(\omega)=$

$F(δ(2t)) (w) + F (\sin(3t))(\omega)=$

$\frac 12 F(δ(t))(\frac \omega2)+\frac13 F(\sin(t))(\frac ω3)$

Until here i understand (Theres nothing much to not understand to be honest) But then he immediately jumps into

$\frac 12 + iπ(δ(−2πω − 3) − δ(3 − 2\pi\omega)=$

And i dont understand how he did the last step Can you help me?