we are asked in the problem to solve for x in the expression tan(x+π)+2sin(x+π) = 0. tan theta is equal to sin theta over cos theta. Hence, the expression results to tan (x+π) = sin (x+π) / cos (x+π) = -2sin (x+π). Thus, 1/cos (x+π) = -2. cos (x+π) = -1/2, cosine becomes negative in the third and fourth quadrants. cosine is 1/2 when the terminal angle is pi/3. x is equal to pi/3 then and 5 pi/6.