find the complete solution for it :-tanx + tany = 4,tan3x + tan3y =2

First use the identity of tan3A and open both the tan3x and tan3y take the LCM solve the numerator and take the denominator to the LHS and open it as well.

Then in the numerator take things common such that each of the variable involving tanx or tany or both will be multiplied to (tanx+tany) then put the value of it as 4 (given) then take the LHS to the RHS and subtract.

you will get an quadratic equation in (tanxtany) assume it as t and solve for roots which will come t=7 or -1

tanxtany=7, tanx + tany=4 solve these 2 then solve the other 2 find out the suitable value of  x and y.