I'll show you how to solve for theta2 given theta from the equation
sin(theta2-theta)+exp(-theta2/(omega*tau))*sin(theta)=0
From the graph I guess this is not exactly what is meant. So you have to explain yourself in more detail.
omega = 1;
tau = 100;
theta = linspace(0,pi/2);
fun = @(theta2,theta)sin(theta2-theta)+exp(-theta2/(omega*tau))*sin(theta);
theta20 = pi;
for i = 1:numel(theta)
theta2(i) = fzero(@(theta2)fun(theta2,theta(i)),theta20);
theta20 = theta2(i);
end
plot(theta*180/pi,theta2*180/pi)
xlim([0 90])
