calculus - Using Euler's formula for cos/sin 12 degrees and cos/sin 48 degrees

$(\cos12^\circ+i\sin12^\circ+\cos48^\circ+i\sin48^\circ)$. Using Euler's Formula, turn this into exponential form (i.e. something like $e^{i\frac{5\pi}{12}}$).

Would I need to use the $\cos$ and $\sin$ sum and difference formulas? I tried doing that and it became messy very quickly. Is there an alternative?