first add all the fractions to get one : with common denominator sinasinbsinc and numerator cosbsinb+cosasina+coscsinc

then multiply the fraction by two both numerator and denominator...to get 2sinasinbsinc as denominator and sin(2a)+sin(2b)+sin(2c) as numerator.

then leave the denominator as it is and try to factorize the numerator using sum to product formulas .Dont forget that 2a+2b+2c=360 now...and you have to prove that

sin2a+sin2b+sin2c =4sinasinbsinc this proves your relation.....

so start the job right now....good luck...