| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2009 |
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| Session | November |
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| Topic | Addition & Double Angle Formulae |
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4 The angles \(\alpha\) and \(\beta\) lie in the interval \(0 ^ { \circ } < x < 180 ^ { \circ }\), and are such that
$$\tan \alpha = 2 \tan \beta \quad \text { and } \quad \tan ( \alpha + \beta ) = 3 .$$
Find the possible values of \(\alpha\) and \(\beta\).