Usage

$$e^{\imath \theta} = \cos \theta + \imath \sin \theta$$ (1)

becomes, upon substituting $-\phi$ for $\theta$

$$e^{-\imath \phi} = \cos \phi + \imath \sin -\phi$$ (2)

or,

$$e^{-\imath \theta} = \cos \theta - \imath \sin \theta$$ (3)

since it doesn't matter what letter we have on each side of the equation, and the sine is an odd function (cosine is even).