If none of α , β , γ , and δ are equal to each other,then tan ( α − β ) tan ( γ − δ ) + tan ( α − γ ) tan ( δ − β ) + tan ( α − δ ) tan ( β − γ ) + tan ( α − β ) tan ( α − γ ) ( tan ( α − δ ) tan ( γ − δ ) tan ( δ − β ) ( tan ( β − γ ) = ?
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Can you provide any approach to prove that the answer is independent of variables (other than bashing) ?
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Answer is independent of α , β , γ , δ .
So, for quick solving, substitute α = 9 0 , β = 4 5 , γ = 4 5 , δ = 4 5