How can I solve simultaneous trigonometric equations involving cosine and sine?

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How would one go about solving the following equation?

242= 290cos(theta) + 187cos(phi)
0 = 290sin(theta) - 187sin(phi)


I have tried squaring both sides of both equations and adding them, and then using cos2x + sin2x = 1 to narrow some stuff down, and basically only found that:

phi + theta = 123.9 degrees.

But I still feel like I'm stuck. Maybe I'm missing an identity or something, I am terrible with those. Any help would be appreciated.
 
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Just realized I put this in the wrong forum,...sorry guys.
 
Since this is homework, here are some strategy hints

Call your equations above 1,2,3

From 1 get cos\phi in terms of cos\theta

From 2 get sin\phi in terms of sin\theta

substitute into either the formula for

cos (\theta + \phi)

or

sin (\theta + \phi)

Substituting into 3 will get you an equation in a single unknown.
 

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