Consider the expression, tan‌2‌α‌tan‌2‌β+tan‌2‌β‌tan‌2‌γ+tan‌2‌γ‌tan‌2‌α=1 tan‌2‌α[
tan‌2‌β+tan‌2‌γ
1+tan‌2‌β‌tan‌2‌γ
]=1 tan‌2‌α‌tan(2β+2γ)=1 tan(2β+2γ)=cos‌2‌α Substitute 15° for β,12° for α and 18° for γ. tan(30+36)=cot‌24 tan‌66°=tan(90°−66°) tan‌66°=tan‌66° The above equation is true so,