#knowns

Theta$\_2=(37*$np$.$pi$)/180$

R$\_$OA$=2$

R$\_$AB$=4\mathrm{.}5$

R$\_$CB$=3\mathrm{.}1$

R$\_$OC$=4$

R$\_$AP$=2\mathrm{.}5$

ALPHA$=(27*$np$.$pi$)/180$

# Define the equations as functions

def equations$($vars$)$:

Theta$\_3,$ Theta$\_4=$ vars

eq$1=-$R$\_$OA $*$ np$.$cos$($Theta$\_2)+$ R$\_$AB $*$ np$.$cos$($Theta$\_3)-$ R$\_$CB $*$ np$.$cos$($Theta$\_4)-$ R$\_$OC $*$ np$.$cos$(0)$

eq$2=-$R$\_$OA $*$ np$.$sin$($Theta$\_2)+$ R$\_$AB $*$ np$.$sin$($Theta$\_3)-$ R$\_$CB $*$ np$.$sin$($Theta$\_4)-$ R$\_$OC $*$ np$.$sin$(0)$

# eq$1=$ r$\_$O$2$A $*$ np$.$cos$($Theta$\_$O$2$A$)+$ r$\_$AB $*$ np$.$cos$($Theta$\_$AB$)-$ r$\_$O$4$B $*$ np$.$cos$($Theta$\_$O$4$B$)-$ r$\_$O$2$O$4*$ np$.$cos$(0)$

# eq$2=$ r$\_$O$2$A $*$ np$.$sin$($Theta$\_$O$2$A$)+$ r$\_$AB $*$ np$.$sin$($Theta$\_$AB$)-$ r$\_$O$4$B $*$ np$.$sin$($Theta$\_$O$4$B$)-$ r$\_$O$2$O$4*$ np$.$sin$(0)$

return $[$eq$1,$ eq$2]$

# Initial guesses for x and y $($in radians$)$

initial$\_$guess $=[(15*$np$.$pi$)/180,(50*$np$.$pi$)/180]$

# Theta $3$ Theta $4$

# Solve the system of equations

solution $=$ fsolve$($equations$,$ initial$\_$guess$)$

# Convert the solution to degrees for better readability

solution$\_$degrees $=$ np$.$degrees$($solution$)$

# Display the solutions

# print$($f$"$Solution in radians: Theta$\_$AB $=\{$solution$[0]\},$ Theta$\_$O$4$B $=\{$solution$[1]\}")$

print$($f$"$Solution in degrees: Theta$\_3=\{$solution$\_$degrees$[0]\},$ Theta$\_$O$4=\{$solution$\_$degrees$[1]\}")$