To find the value of g(f(pi/3)), you can substitute the value of f(pi/3) into the function g(x). Since f(x) = 2sin x, the value of f(pi/3) is equal to 2sin(pi/3). You can use a calculator or lookup table to find the sine of pi/3, or you can approximate it by using the small angle approximation, which says that the sine of a small angle is approximately equal to the angle in radians. In this case, pi/3 is approximately equal to 1.05 radians, so the value of f(pi/3) is approximately equal to 2sin(1.05) = 2 * 0.95 = 1.9.
Now that you have the value of f(pi/3), you can substitute it into the function g(x) to find the value of g(f(pi/3)). Since g(x) = x^4 - 2, the value of g(f(pi/3)) is equal to (1.9)^4 - 2 = 5.061 - 2 = 3.061.
Therefore, the value of g(f(pi/3)) is approximately 3.061.