writing optimization constraints in MATLAB involving function calls

I am trying to solve following optimization problem:

I am using calculating θ1, θ2 and θ3 for every value of phi discretized between 30 deg. to 150 deg., using following function function thetas = inverse_kinematics_1(l1,l2,l3,phi)

    x = 100;
    y = 0;

    x1 = x - (l3*cos(phi));
    y1 = y - (l3*sin(phi));
    a = sqrt(x1^2 + y1^2);
    y2 = -y1/a;
    x2 = -x1/a;
    gamma = atan2(y2,x2);
    c = (- x1^2 - y1^2 - l1^2 + l2^2)/(2*l1*a);
    d = acos(c);

    theta1 = gamma + d;
    if theta1 < 0
        theta1 = theta1 + 2*pi;
    end

    e = (y1 - l1*sin(theta1))/l2;
    f = (x1 - l1*cos(theta1))/l2;

    theta2 = atan2(e,f) - theta1;
    if theta2 < 0
        theta2 = theta2 + 2*pi;
    end

    theta3 = (phi)- (theta1 + theta2);
    if theta3 < 0
        theta3 = theta3 + 2*pi;
    end

    thetas = [theta1,theta2,theta3].*180/pi;
end

How can I write the constraints in this situation ?