Verified answer

if f(x)=tanx

that means that f(a)=tan(a)=2

Therefore a= arctan (2) ---( that's shift+ tan2 on the calculator)

=1.11

f(-a) = tan(- arctan (2)) = -2 (arc tan is the inverse of the tan so they cancel out)

B= f(a) + f(a + π) + f(a + 2π) = tan(a) +tan(a + π) +tan(a + 2π)

tan(a + π)= 2 (this is because tan is positive in the third quadrant and tan(a) = tan(a + π) because a + π is like the alternate angle of a if you draw a quadrant diagram)

tan(a + 2π)= 2 (tan is positive in the first quadrant)

therefore B= 2+2+2=6

I cant really explain this without diagrams but i hope it helps a bit :)