cos(q)*cos(q)+sin(q)*sin(q)*sin(f)*sin(f)=cos(f)*cos(f) sin(q)*sin(q)=cos(q)*cos(q)*1/(1-cos(f)*cos(f))

$$sin{left (q right )} sin{left (q right )} sin{left (f right )} sin{left (f right )} + cos{left (q right )} cos{left (q right )} = cos{left (f right )} cos{left (f right )}$$

cos(q)*cos(q)
sin(q)*sin(q) = —————–
1 – cos(f)*cos(f)

$$sin{left (q right )} sin{left (q right )} = frac{cos{left (q right )} cos{left (q right )}}{- cos^{2}{left (f right )} + 1}$$

f1 = -2.442407489048769
q1 = -2.142655196996107

f2 = -10.1239631253104
q2 = -5.28424785058590

f3 = 5.584000142638563
q3 = 10.42371541736307

f4 = 2.442407489048769
q4 = 10.42371541736307

f5 = -10.1239631253104
q5 = 5.28424785058590

f6 = -10.1239631253104
q6 = -2.142655196996107

f7 = -5.584000142638563
q7 = 5.28424785058590

f8 = -5.584000142638563
q8 = -5.28424785058590

f9 = -2.442407489048769
q9 = 10.42371541736307

f10 = -2.442407489048769
q10 = 4.14053011018348

f11 = 5.584000142638563
q11 = 5.28424785058590

f12 = -10.1239631253104
q12 = -10.42371541736307

f13 = -10.1239631253104
q13 = 2.142655196996107

f14 = -5.584000142638563
q14 = -2.142655196996107

f15 = 10.1239631253104
q15 = 10.42371541736307

f16 = 2.442407489048769
q16 = 2.142655196996107

f17 = 2.442407489048769
q17 = 4.14053011018348

f18 = -5.584000142638563
q18 = 2.142655196996107

f19 = -10.1239631253104
q19 = 10.42371541736307

f20 = -2.442407489048769
q20 = 2.142655196996107

f21 = -5.584000142638563
q21 = 10.42371541736307