Calculate $\sin{55}-\sin{19}+\sin{53}-\sin{17}$ without calculator So here is a trigonometric series.

$$\sin{55^\mathrm{o}}-\sin{19^\mathrm{o}}+\sin{53^\mathrm{o}}-\sin{17^\mathrm{o}}$$

Strange isn't it,  and I have to calculate the total result of the series (without calculator). I don't think Maclaurin series will help me any way. Further I tried almost all trigonometric identities (as per my knowledge) but so far I had no clue. Probably I am missing some kind of identity. Anyone can help me in this?

Note: It's not a homework question.


Hint: 
The key observation here is that $55+17=53+19$.
$$\sin{55}^\circ-\sin{19}^\circ+\sin{53}^\circ-\sin{17}^\circ=\color{#C00}{\sin55^\circ-\sin17^\circ}+\color{green}{\sin53^\circ-\sin19^\circ}.$$
Now use the identity
$$\sin a-\sin b=2\sin(\tfrac{a-b}2)\cos({\tfrac{a+b}2}).$$
