restart; 1 

`:=`(f, proc (theta) options operator, arrow; `+`(`*`(`/`(2, 3), `*`(cos(theta))), `*`(`/`(1, 3), `*`(theta))) end proc); 1 

proc (theta) options operator, arrow; `+`(`*`(`/`(2, 3), `*`(cos(theta))), `*`(`/`(1, 3), `*`(theta))) end proc (1)
 

`:=`(df, diff(f(theta), theta)); 1 

`+`(`-`(`*`(`/`(2, 3), `*`(sin(theta)))), `/`(1, 3)) (2)
 

solve(df = 0, theta); 1 

`+`(`*`(`/`(1, 6), `*`(Pi))) (3)
 

plot(f(theta), theta = 0 .. `+`(`*`(`/`(1, 2), `*`(Pi)))); 1 

Plot_2d
 

evalf(f(0)); 1 

.6666666667 (4)
 

evalf(f(`+`(`*`(`/`(1, 2), `*`(Pi))))); 1 

.5235987758 (5)
 

`:=`(g, proc (theta) options operator, arrow; `+`(`*`(`/`(1, 3), `*`(cos(theta))), `*`(`/`(2, 3), `*`(theta))) end proc); 1 

proc (theta) options operator, arrow; `+`(`*`(`/`(1, 3), `*`(cos(theta))), `*`(`/`(2, 3), `*`(theta))) end proc (6)
 

`:=`(dg, diff(g(theta), theta)); 1 

`+`(`-`(`*`(`/`(1, 3), `*`(sin(theta)))), `/`(2, 3)) (7)
 

solve(dg = 0, theta); 1 

arcsin(2) (8)
 

plot(g(theta), theta = 0 .. `+`(`*`(`/`(1, 2), `*`(Pi)))); 1 

Plot_2d