Since sin(pi + pi/6) = -sin(pi/6) = -1/2 and sin(2pi - pi/6) = -sin(pi/6) = -1/2, one can see from the graph that the solutions to sin(y) = -1/2 are y = 7pi/6 + 2pi * k and 11pi/6 + 2pi * k for all integer k. Then the roots of the original equation can be found from .77x = y.