How to find Fourier Series Coefficients
First, recognise that the fundamental period of the signal x(t) (sum of two sinusoidals with periods 2/3 s and 1/50 s) is 2s. And the fundamental frequency, $f_0$, is 0.5 hz.  

Then considering the CT Fourier Series expansion of the periodic signal x(t) wrt its fundamental frequency $f_0$ given as $\sum_{-\infty}^{\infty}{a_k e^{jk2\pi f_0t}}$ you can  therefore find the coefficients corresponding to $2\cos(3\pi t)$ and $\sin(100\pi t + \pi/3)$ with k=3 and k=100 respectively. 

Then, by expressing the sinusoidals in terms of complex exponentials using the Euler's identity this becomes $a_3=1 ,~ a_{-3}= 1 , ~~a_{100} = e^{j\pi/3}/2j, ~~a_{-100} = -e^{-j\pi/3}/2j $  which can be further manipulated if you want a rectengular representation of the complex coefficient instead of the above mixed-polar one.

Assuming no errors made during the arithmetic.