Given that \(\alpha\) is the acute angle such that \(\tan \alpha = \frac { 2 } { 5 }\), find the exact value of \(\cos \alpha\).
Given that \(\beta\) is the obtuse angle such that \(\sin \beta = \frac { 3 } { 7 }\), find the exact value of \(\cos \beta\).
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The diagram shows a triangle \(A B C\) with \(A C = 6 \mathrm {~cm} , B C = 8 \mathrm {~cm}\), angle \(B A C = 60 ^ { \circ }\) and angle \(A B C = \gamma\). Find the exact value of \(\sin \gamma\), simplifying your answer.