What could be the mathematical equation of the given signal? We know that Fourier series for periodic signal $y(t)$ is given by
$$ y(t) = \sum\limits_{m=0}^{+\infty} a_m \cos(w_m t) + \sum\limits_{m=0}^{+\infty}b_m \sin(w_m t). \quad (2)$$
Now,I want to find Fourier series of a periodic sinusoidal signal 
$y(t)$ given below. But I don't understand how should I decide what are the harmonics present and how to calculate Fourier coefficients.

So what could be the mathematical equation of the given signal ?
Note: if there is any way than Fourier series to express the given signal in the form of mathematical equation  ,you can  explain with other way also.

You can calculate it's Fast Fourier Transform, but choose to only calculate the frequencies you need.
To express Fourier series in terms of a continous Fourier transform, we need to introduce Theory of distributions as the fourier transform of sines and cosines are sums of Dirac distributions. If we are fine with considering the discrete fourier transform (DFT) then fourier series and the DFT coincide.
Combine this with the fact that the Fourier transform is linear and you will be done.
