+118723 Hi Max, it is nice to meet you :)
I will assume degrees
\(cos^25+cos^210+..... cos^245+........+cos^280+cos^285\\ =cos^25+cos^210+..... cos^245+........+sin^210+sin^25\\ =cos^25+sin^25+cos^210+sin^210+.........+cos^240+sin^240+cos^245\\ =1+1+1+1+1+1+1+1+cos^45\\ =8+\frac{1}{\sqrt2}\\ =8+\frac{\sqrt2}{2}\\ =\frac{16+\sqrt2}{2}\\ \)
