Solving of system of trigonometric equation

[Андрей Ширшов]

Hi!
I'd like to solve the following system of trigonometric equation:

(R+r)*cos(gamma1) + r*cos(k*gamma1+alpha_0) == (R+r)*cos(gamma2) + r*cos(k*gamma2+alpha_1)
(R+r)*cos(gamma1) + r*cos(k*gamma1+alpha_0) == (R+r)*cos(gamma2) + r*cos(k*gamma2+alpha_1)

where:

gamma1, gamma2 = var('gamma1, gamma2')
R=100
r=10
k=30
alpha_0 = 0
alpha_1 = pi/2

I tried the followin code:

R = 100
r = 10
k = 30
alpha_0 = 0
alpha_1 = pi/2
gamma1, gamma2 = var('gamma1, gamma2')

solve([(R+r)*cos(gamma1) + r*cos(k*gamma1+alpha_0) - (R+r)*cos(gamma2) + r*cos(k*gamma2+alpha_1), (R+r)*cos(gamma1) + r*cos(k*gamma1+alpha_0) - (R+r)*cos(gamma2) + r*cos(k*gamma2+alpha_1)], (gamma1, gamma2))

Sympy solve it too long and I can't wait for result.

Thanks in advance, Andrei.