Thanks kindly for helping
The constants are listed before the 3 equations. The variables to solve for are r, R, and phi for a specified theta. The derivatives I took to be (theta-theta_0)/(phi-phi_0) etc. for the initial and calculated values.
I have used some Maple code and some just to demonstrate the equations.
L:=99994.44;# a constant based on flow properties
Equation 1: R_1=r/sin(theta)*(1.4*3.4^2*I1+L*I2)/(r^2*(1+1.4*3.4^2*sin(phi)^2)-L*sin(theta-phi)^2*cos(1.57/Theta*theta)^4.545);
Equation 2: R*sin(theta-phi)=(r*((d(theta)/d(phi)));
Equation 3: (r*cot(theta-phi))=(-(d(r)/d(theta))
I can maybe implement Broydons method or some similar numerical method but if there is a better Maple method that would be good to know.