Find the values of A between and including 0 and 360 degrees for tan(2A) = 3tan(A)

You cannot work with this equation in the current form so you must use identities to find an equivalent form that you can work with. It is known that tan(2A) = 2tan(A) / 1-tan²(A) so set this equal to 3tan(A), multiply the denominator to the other side and with some rearrangement you will get 3tan³(A) - tan(A) = 0. Now it should hopefully be clear that you can factorise out tan(A) and you will get two solutions of tan(A) = 0 and 3tan²(A) - 1 = 0. The second term equates to tan(A) = +and- (1/3)^0.5. The final step is to sketch a graph of y = tan(A) and using that with the inverse tan function on your calculator you should get the desired values within the required range as 0^o, 180^o, 360^o, 30^o, 210^o, 150^o, 330^o.