I have stumbled upon a problem for which I need some help. I am trying to solve an equation which is basically a function of (theta1 and theta2). The function has the following functional form:

f[theta1_,theta2_] := -(Cos[phi - theta1]) - (Cos[phi - theta2]) + (((Sin[theta1]^2) + (Sin[theta2]^2))) + Cos[theta1 - theta2]; 

I have to do the following steps: 1. Do first-order derivative for f(theta1, theta2) with respect to theta1 and theta2. 2. Put first order derivatives to zero and solve for theta1 and theta2. 3. Compute second-order derivatives and check the sign of the second-order derivative for obtained theta1 and theta2.

To compute the first order derivative, I have used the following command:

Solve[{D[f[theta1_, theta2_], theta1] == 0 && D[f[theta1_, theta2_], theta2] == 0}, {theta1, theta2}] 

However, solve returns the following error:

Solve::inex: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help.

And followed by:

Solve[{0.08 Sin[theta1_] (Pattern^(1,0))[theta1,]+1/500 Cos[theta1] Sin[theta1_] (Pattern^(1,0))[theta1,]-5 Sin[theta1-theta2_] (Pattern^(1,0))[theta1,]==0&&5 Sin[theta1-theta2_] (Pattern^(1,0))[theta2,]+0.08 Sin[theta2] (Pattern^(1,0))[theta2,]+1/500 Cos[theta2] Sin[theta2_] (Pattern^(1,0))[theta2,_]==0},{theta1,theta2}]

Any help will be highly appreciated. Thank you for your co-operation!!

Cheers!!